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<div class="vector-toc-text"> 3 Syntax </div> </a> <button aria-controls="toc-Syntax-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Syntax subsection </button> <ul id="toc-Syntax-sublist" class="vector-toc-list"> <li id="toc-"Hello,_world!"_example" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#"Hello,_world!"_example"> <div class="vector-toc-text"> 3.1 "Hello, world!" example </div> </a> <ul id="toc-"Hello,_world!"_example-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variables" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Variables"> <div class="vector-toc-text"> 3.2 Variables </div> </a> <ul id="toc-Variables-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vectors_and_matrices" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vectors_and_matrices"> <div class="vector-toc-text"> 3.3 Vectors and matrices </div> </a> <ul id="toc-Vectors_and_matrices-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Structures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Structures"> <div class="vector-toc-text"> 3.4 Structures </div> </a> <ul id="toc-Structures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Functions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Functions"> <div class="vector-toc-text"> 3.5 Functions </div> </a> <ul id="toc-Functions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Function_handles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Function_handles"> <div class="vector-toc-text"> 3.6 Function handles </div> </a> <ul id="toc-Function_handles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Classes_and_object-oriented_programming" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Classes_and_object-oriented_programming"> <div class="vector-toc-text"> 3.7 Classes and object-oriented programming </div> </a> <ul id="toc-Classes_and_object-oriented_programming-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Graphics_and_graphical_user_interface_programming" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Graphics_and_graphical_user_interface_programming"> <div class="vector-toc-text"> 4 Graphics and graphical user interface programming </div> </a> <ul id="toc-Graphics_and_graphical_user_interface_programming-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-MATLAB_and_other_languages" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#MATLAB_and_other_languages"> <div class="vector-toc-text"> 5 MATLAB and other languages </div> </a> <ul id="toc-MATLAB_and_other_languages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relations_to_US_sanctions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relations_to_US_sanctions"> <div class="vector-toc-text"> 6 Relations to US sanctions </div> </a> <ul id="toc-Relations_to_US_sanctions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 7 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> 8 Notes </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 9 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 10 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">MATLAB</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 70 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-70" aria-hidden="true" > 70 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%A7%D8%AA%D9%84%D8%A7%D8%A8" title="ماتلاب – Arabic" lang="ar" hreflang="ar" data-title="ماتلاب" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/MATLAB" title="MATLAB – Azerbaijani" lang="az" hreflang="az" data-title="MATLAB" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%9F%E0%A6%B2%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AC" title="ম্যাটল্যাব – Bangla" lang="bn" hreflang="bn" data-title="ম্যাটল্যাব" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/MATLAB" title="MATLAB – Minnan" lang="nan" hreflang="nan" data-title="MATLAB" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/MATLAB" title="MATLAB – Bulgarian" lang="bg" hreflang="bg" data-title="MATLAB" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/MATLAB" title="MATLAB – Bosnian" lang="bs" hreflang="bs" data-title="MATLAB" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/MATLAB" title="MATLAB – Catalan" lang="ca" hreflang="ca" data-title="MATLAB" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/MATLAB" title="MATLAB – Czech" lang="cs" hreflang="cs" data-title="MATLAB" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/MATLAB" title="MATLAB – Danish" lang="da" hreflang="da" data-title="MATLAB" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Matlab" title="Matlab – German" lang="de" hreflang="de" data-title="Matlab" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/MATLAB" title="MATLAB – Estonian" lang="et" hreflang="et" data-title="MATLAB" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/MATLAB" title="MATLAB – Greek" lang="el" hreflang="el" data-title="MATLAB" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/MATLAB" title="MATLAB – Spanish" lang="es" hreflang="es" data-title="MATLAB" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/MATLAB" title="MATLAB – Esperanto" lang="eo" hreflang="eo" data-title="MATLAB" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/MATLAB" title="MATLAB – Basque" lang="eu" hreflang="eu" data-title="MATLAB" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AA%D9%84%D8%A8" title="متلب – Persian" lang="fa" hreflang="fa" data-title="متلب" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/MATLAB" title="MATLAB – French" lang="fr" hreflang="fr" data-title="MATLAB" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A7%A4%ED%8A%B8%EB%9E%A9" title="매트랩 – Korean" lang="ko" hreflang="ko" data-title="매트랩" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A9%D5%AC%D5%A1%D5%A2" title="Մաթլաբ – Armenian" lang="hy" hreflang="hy" data-title="Մաթլաբ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A5%88%E0%A4%9F%E0%A4%B2%E0%A5%88%E0%A4%AC" title="मैटलैब – Hindi" lang="hi" hreflang="hi" data-title="मैटलैब" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/MATLAB" title="MATLAB – Croatian" lang="hr" hreflang="hr" data-title="MATLAB" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/MATLAB" title="MATLAB – Indonesian" lang="id" hreflang="id" data-title="MATLAB" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/MATLAB" title="MATLAB – Icelandic" lang="is" hreflang="is" data-title="MATLAB" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/MATLAB" title="MATLAB – Italian" lang="it" hreflang="it" data-title="MATLAB" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/MATLAB" title="MATLAB – Hebrew" lang="he" hreflang="he" data-title="MATLAB" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AE%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%9F%E0%B2%B2%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%AC" title="ಮ್ಯಾಟಲ್ಯಾಬ – Kannada" lang="kn" hreflang="kn" data-title="ಮ್ಯಾಟಲ್ಯಾಬ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/MATLAB" title="MATLAB – Latvian" lang="lv" hreflang="lv" data-title="MATLAB" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/MATLAB" title="MATLAB – Lithuanian" lang="lt" hreflang="lt" data-title="MATLAB" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/MATLAB" title="MATLAB – Lombard" lang="lmo" hreflang="lmo" data-title="MATLAB" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/MATLAB" title="MATLAB – Hungarian" lang="hu" hreflang="hu" data-title="MATLAB" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/MATLAB" title="MATLAB – Macedonian" lang="mk" hreflang="mk" data-title="MATLAB" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AE%E0%B4%BE%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%8D%E2%80%8C%E0%B4%B2%E0%B4%BE%E0%B4%AC%E0%B5%8D" title="മാറ്റ്‌ലാബ് – Malayalam" lang="ml" hreflang="ml" data-title="മാറ്റ്‌ലാബ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AE%E0%A5%85%E0%A4%9F%E0%A4%B2%E0%A5%85%E0%A4%AC" title="मॅटलॅब – Marathi" lang="mr" hreflang="mr" data-title="मॅटलॅब" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/MATLAB" title="MATLAB – Malay" lang="ms" hreflang="ms" data-title="MATLAB" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/MATLAB" title="MATLAB – Burmese" lang="my" hreflang="my" data-title="MATLAB" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/MATLAB" title="MATLAB – Dutch" lang="nl" hreflang="nl" data-title="MATLAB" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/MATLAB" title="MATLAB – Japanese" lang="ja" hreflang="ja" data-title="MATLAB" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/MATLAB" title="MATLAB – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="MATLAB" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/MATLAB" title="MATLAB – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="MATLAB" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AE%E0%AD%8D%E0%AD%9F%E0%AC%BE%E0%AC%9F%E0%AD%8D%E2%80%8C%E0%AC%B2%E0%AC%BE%E0%AC%AC%E0%AD%8D%E2%80%8C" title="ମ୍ୟାଟ୍‌ଲାବ୍‌ – Odia" lang="or" hreflang="or" data-title="ମ୍ୟାଟ୍‌ଲାବ୍‌" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target">ଓଡ଼ିଆ</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/MATLAB" title="MATLAB – Uzbek" lang="uz" hreflang="uz" data-title="MATLAB" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/MATLAB" title="MATLAB – Polish" lang="pl" hreflang="pl" data-title="MATLAB" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/MATLAB" title="MATLAB – Portuguese" lang="pt" hreflang="pt" data-title="MATLAB" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/MATLAB" title="MATLAB – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="MATLAB" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target">Qaraqalpaqsha</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/MATLAB" title="MATLAB – Romanian" lang="ro" hreflang="ro" data-title="MATLAB" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/MATLAB" title="MATLAB – Russian" lang="ru" hreflang="ru" data-title="MATLAB" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/MATLAB" title="MATLAB – Scots" lang="sco" hreflang="sco" data-title="MATLAB" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Matlab" title="Matlab – Albanian" lang="sq" hreflang="sq" data-title="Matlab" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/MATLAB" title="MATLAB – Simple English" lang="en-simple" hreflang="en-simple" data-title="MATLAB" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/MATLAB" title="MATLAB – Slovak" lang="sk" hreflang="sk" data-title="MATLAB" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/MATLAB" title="MATLAB – Slovenian" lang="sl" hreflang="sl" data-title="MATLAB" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%D8%A7%D8%AA%D9%84%D8%A7%D8%A8" title="ماتلاب – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ماتلاب" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/MATLAB" title="MATLAB – Serbian" lang="sr" hreflang="sr" data-title="MATLAB" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/MATLAB" title="MATLAB – Serbo-Croatian" lang="sh" hreflang="sh" data-title="MATLAB" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/MATLAB" title="MATLAB – Finnish" lang="fi" hreflang="fi" data-title="MATLAB" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Matlab" title="Matlab – Swedish" lang="sv" hreflang="sv" data-title="Matlab" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/MATLAB" title="MATLAB – Tagalog" lang="tl" hreflang="tl" data-title="MATLAB" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%87%E0%AE%9F%E0%AF%8D%E0%AE%B2%E0%AF%87%E0%AE%AA%E0%AF%8D" title="மேட்லேப் – Tamil" lang="ta" hreflang="ta" data-title="மேட்லேப்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/MATLAB" title="MATLAB – Kabyle" lang="kab" hreflang="kab" data-title="MATLAB" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target">Taqbaylit</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%A1%E0%B8%95%E0%B9%81%E0%B8%A5%E0%B9%87%E0%B8%9A" title="แมตแล็บ – Thai" lang="th" hreflang="th" data-title="แมตแล็บ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/MATLAB" title="MATLAB – Tajik" lang="tg" hreflang="tg" data-title="MATLAB" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/MATLAB" title="MATLAB – Turkish" lang="tr" hreflang="tr" data-title="MATLAB" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/MATLAB" title="MATLAB – Turkmen" lang="tk" hreflang="tk" data-title="MATLAB" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target">Türkmençe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/MATLAB" title="MATLAB – Ukrainian" lang="uk" hreflang="uk" data-title="MATLAB" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%DB%8C%D9%B9%D9%84%DB%8C%D8%A8" title="میٹلیب – Urdu" lang="ur" hreflang="ur" data-title="میٹلیب" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D9%85%DB%95%D8%AA%D9%84%DB%95%D8%A8" title="مەتلەب – Uyghur" lang="ug" hreflang="ug" data-title="مەتلەب" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target">ئۇيغۇرچە / Uyghurche</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/MATLAB" title="MATLAB – Vietnamese" lang="vi" hreflang="vi" data-title="MATLAB" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/MATLAB" title="MATLAB – Wu" lang="wuu" hreflang="wuu" data-title="MATLAB" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/MATLAB" title="MATLAB – Cantonese" lang="yue" hreflang="yue" data-title="MATLAB" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/MATLAB" 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Numerical computing environment and programming language</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the geographical region, see <a href="/wiki/Matlab_(Bangladesh)" title="Matlab (Bangladesh)">Matlab (Bangladesh)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/MATHLAB" title="MATHLAB">MATHLAB</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vevent"><caption class="infobox-title summary">MATLAB (software)</caption><tbody><tr><td colspan="2" class="infobox-image logo"><a href="/wiki/File:Matlab_Logo.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Matlab_Logo.png/250px-Matlab_Logo.png" decoding="async" width="150" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Matlab_Logo.png/330px-Matlab_Logo.png 2x" data-file-width="2529" data-file-height="2264" /></a><div class="infobox-caption">L-shaped membrane logo<a href="#cite_note-1">[1]</a></div></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Programmer" title="Programmer">Developer(s)</a></th><td class="infobox-data"><a href="/wiki/MathWorks" title="MathWorks">MathWorks</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Initial release</th><td class="infobox-data">1984; 41 years ago (1984)</td></tr><tr style="display: none;"><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" /></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">R2024b<a href="#cite_note-wikidata-fffd30ea8904b8de0ddda28ec8606f786b540de9-v18-2">[2]</a> <a href="https://www.wikidata.org/wiki/Q169478?uselang=en#P348" title="Edit this on Wikidata"><img alt="Edit this on Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a> / September 12, 2024; 6 months ago (September 12, 2024)</div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Written in</th><td class="infobox-data"><a href="/wiki/C_(programming_language)" title="C (programming language)">C</a>/<a href="/wiki/C%2B%2B" title="C++">C++</a>, MATLAB</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Operating_system" title="Operating system">Operating system</a></th><td class="infobox-data"><a href="/wiki/Microsoft_Windows" title="Microsoft Windows">Windows</a>, <a href="/wiki/MacOS" title="MacOS">macOS</a>, and <a href="/wiki/Linux" title="Linux">Linux</a><a href="#cite_note-3">[3]</a><a href="#cite_note-4">[4]</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Computing_platform" title="Computing platform">Platform</a></th><td class="infobox-data"><a href="/wiki/IA-32" title="IA-32">IA-32</a>, <a href="/wiki/X86-64" title="X86-64">x86-64</a>, <a href="/wiki/ARM64" class="mw-redirect" title="ARM64">ARM64</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_categories#Categorization_approaches" title="Software categories">Type</a></th><td class="infobox-data"><a href="/wiki/List_of_numerical-analysis_software" title="List of numerical-analysis software">Numerical computing</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_license" title="Software license">License</a></th><td class="infobox-data"><a href="/wiki/Proprietary_software" title="Proprietary software">Proprietary</a> <a href="/wiki/Commercial_software" title="Commercial software">commercial software</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Website</th><td class="infobox-data"><a rel="nofollow" class="external text" href="https://www.mathworks.com/products/matlab.html">mathworks.com</a></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" /><table class="infobox vevent"><caption class="infobox-title summary">MATLAB (programming language)</caption><tbody><tr><th scope="row" class="infobox-label"><a href="/wiki/Programming_paradigm" title="Programming paradigm">Paradigm</a></th><td class="infobox-data"><a href="/wiki/Multi-paradigm_programming_language" class="mw-redirect" title="Multi-paradigm programming language">multi-paradigm</a>: <a href="/wiki/Functional_programming" title="Functional programming">functional</a>, <a href="/wiki/Imperative_programming" title="Imperative programming">imperative</a>, <a href="/wiki/Procedural_programming" title="Procedural programming">procedural</a>, <a href="/wiki/Object-oriented_programming" title="Object-oriented programming">object-oriented</a>, <a href="/wiki/Array_programming" title="Array programming">array</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Software_design" title="Software design">Designed by</a></th><td class="infobox-data"><a href="/wiki/Cleve_Moler" title="Cleve Moler">Cleve Moler</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Software_developer" class="mw-redirect" title="Software developer">Developer</a></th><td class="infobox-data organiser"><a href="/wiki/MathWorks" title="MathWorks">MathWorks</a></td></tr><tr><th scope="row" class="infobox-label">First appeared</th><td class="infobox-data">late 1970s</td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" /></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">R2024b<a href="#cite_note-wikidata-fffd30ea8904b8de0ddda28ec8606f786b540de9-v18-2">[2]</a> <a href="https://www.wikidata.org/wiki/Q169478?uselang=en#P348" title="Edit this on Wikidata"><img alt="Edit this on Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a> / September 12, 2024; 6 months ago (September 12, 2024)</div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Type_system" title="Type system">Typing discipline</a></th><td class="infobox-data"><a href="/wiki/Dynamic_typing" class="mw-redirect" title="Dynamic typing">dynamic</a>, <a href="/wiki/Weak_typing" class="mw-redirect" title="Weak typing">weak</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Filename_extension" title="Filename extension">Filename extensions</a></th><td class="infobox-data"><code>.m</code>, <code>.p</code>,<a href="#cite_note-5">[5]</a> <code>.mex*</code>,<a href="#cite_note-6">[6]</a> <code>.mat</code>,<a href="#cite_note-7">[7]</a> <code>.fig</code>,<a href="#cite_note-8">[8]</a> <code>.mlx</code>,<a href="#cite_note-9">[9]</a> <code>.mlapp</code>,<a href="#cite_note-10">[10]</a> <code>.mltbx</code>,<a href="#cite_note-11">[11]</a> <code>.mlappinstall</code>,<a href="#cite_note-12">[12]</a> <code>.mlpkginstall</code><a href="#cite_note-13">[13]</a></td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><a rel="nofollow" class="external text" href="https://www.mathworks.com/products/matlab.html">mathworks.com</a></td></tr><tr><th colspan="2" class="infobox-header" style="background-color: #eee;">Influenced by</th></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><div class="hlist"> <ul><li><a href="/wiki/APL_(programming_language)" title="APL (programming language)">APL</a></li> <li><a href="/wiki/EISPACK" title="EISPACK">EISPACK</a></li> <li><a href="/wiki/Fortran" title="Fortran">Fortran</a></li> <li><a href="/wiki/LINPACK" title="LINPACK">LINPACK</a></li> <li><a href="/wiki/PL/0" title="PL/0">PL/0</a></li> <li><a href="/wiki/Speakeasy_(computational_environment)" title="Speakeasy (computational environment)">Speakeasy</a><a href="#cite_note-14">[14]</a></li></ul> </div></td></tr><tr><th colspan="2" class="infobox-header" style="background-color: #eee;">Influenced</th></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><div class="hlist"> <ul><li><a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a><a href="#cite_note-Julia-15">[15]</a></li> <li><a href="/wiki/GNU_Octave" title="GNU Octave">Octave</a><a href="#cite_note-Octave-16">[16]</a></li> <li><a href="/wiki/Scilab" title="Scilab">Scilab</a><a href="#cite_note-Scilab-17">[17]</a></li></ul> </div></td></tr><tr><td colspan="2" class="infobox-below hlist" style="border-top: 1px solid #aaa; padding-top: 3px;"> <ul><li><a href="/wiki/File:Wikibooks-logo-en-noslogan.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/16px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/24px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/32px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></a> <a href="https://en.wikibooks.org/wiki/MATLAB_Programming" class="extiw" title="wikibooks:MATLAB Programming">MATLAB Programming</a> at Wikibooks</li></ul> </td></tr></tbody></table> MATLAB (an abbreviation of "MATrix LABoratory"<a href="#cite_note-18">[18]</a>) is a <a href="/wiki/Proprietary_software" title="Proprietary software">proprietary</a> <a href="/wiki/Multi-paradigm_programming_language" class="mw-redirect" title="Multi-paradigm programming language">multi-paradigm</a> <a href="/wiki/Programming_language" title="Programming language">programming language</a> and <a href="/wiki/Numerical_analysis" title="Numerical analysis">numeric computing</a> environment developed by <a href="/wiki/MathWorks" title="MathWorks">MathWorks</a>. MATLAB allows <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a> manipulations, plotting of <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">functions</a> and data, implementation of <a href="/wiki/Algorithm" title="Algorithm">algorithms</a>, creation of <a href="/wiki/User_interface" title="User interface">user interfaces</a>, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the <a href="/wiki/MuPAD" title="MuPAD">MuPAD</a> <a href="/wiki/Computer_algebra_system" title="Computer algebra system">symbolic engine</a> allowing access to <a href="/wiki/Symbolic_computing" class="mw-redirect" title="Symbolic computing">symbolic computing</a> abilities. An additional package, <a href="/wiki/Simulink" title="Simulink">Simulink</a>, adds graphical multi-domain simulation and <a href="/wiki/Model-based_design" title="Model-based design">model-based design</a> for <a href="/wiki/Dynamical_system" title="Dynamical system">dynamic</a> and <a href="/wiki/Embedded_system" title="Embedded system">embedded systems</a>. As of 2020<a class="external text" href="https://en.wikipedia.org/w/index.php?title=MATLAB&action=edit">[update]</a>, MATLAB has more than four million users worldwide.<a href="#cite_note-mathworksCompanyOverview-19">[19]</a> They come from various backgrounds of <a href="/wiki/Engineering" title="Engineering">engineering</a>, <a href="/wiki/Science" title="Science">science</a>, and <a href="/wiki/Economics" title="Economics">economics</a>. As of 2017<a class="external text" href="https://en.wikipedia.org/w/index.php?title=MATLAB&action=edit">[update]</a>, more than 5000 global colleges and universities use MATLAB to support instruction and research.<a href="#cite_note-20">[20]</a> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=1" title="Edit section: History">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Origins">Origins</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=2" title="Edit section: Origins">edit</a>]</div> MATLAB was invented by mathematician and computer programmer <a href="/wiki/Cleve_Moler" title="Cleve Moler">Cleve Moler</a>.<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a> The idea for MATLAB was based on his 1960s PhD <a href="/wiki/Thesis" title="Thesis">thesis</a>.<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a> Moler became a math professor at the <a href="/wiki/University_of_New_Mexico" title="University of New Mexico">University of New Mexico</a> and started developing MATLAB for his students<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a> as a hobby.<a href="#cite_note-hobby-22">[22]</a> He developed MATLAB's initial <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a> programming in 1967 with his one-time thesis advisor, <a href="/wiki/George_Forsythe" title="George Forsythe">George Forsythe</a>.<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a> This was followed by <a href="/wiki/Fortran" title="Fortran">Fortran</a> code for <a href="/wiki/Linear_equation" title="Linear equation">linear equations</a> in 1971.<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a> Before version 1.0, MATLAB "was not a programming language; it was a simple interactive <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a> calculator. There were no programs, no toolboxes, no graphics. And no <a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">ODEs</a> or <a href="/wiki/FFT" class="mw-redirect" title="FFT">FFTs</a>."<a href="#cite_note-23">[23]</a> The first early version of MATLAB was completed in the late 1970s.<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a> The software was disclosed to the public for the first time in February 1979 at the <a href="/wiki/Naval_Postgraduate_School" title="Naval Postgraduate School">Naval Postgraduate School</a> in California.<a href="#cite_note-hobby-22">[22]</a> Early versions of MATLAB were simple <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix calculators</a> with 71 pre-built functions.<a href="#cite_note-Moler_Little_pp._1–67-24">[24]</a> At the time, MATLAB was distributed for free<a href="#cite_note-Xue_Press_2020_p._21-25">[25]</a><a href="#cite_note-Press_2008_p._6-26">[26]</a> to universities.<a href="#cite_note-Woodford_Phillips_2011_p._1-27">[27]</a> Moler would leave copies at universities he visited and the software developed a strong following in the math departments of university campuses.<a href="#cite_note-Tranquillo_2011_p.-28">[28]</a>: 5  In the 1980s, Cleve Moler met <a href="/wiki/John_N._Little" title="John N. Little">John N. Little</a>. They decided to reprogram MATLAB in <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> and market it for the <a href="/wiki/IBM" title="IBM">IBM</a> <a href="/wiki/Desktop_computer" title="Desktop computer">desktops</a> that were replacing <a href="/wiki/Mainframe_computer" title="Mainframe computer">mainframe computers</a> at the time.<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a> John Little and programmer Steve Bangert re-programmed MATLAB in C, created the MATLAB programming language, and developed features for toolboxes.<a href="#cite_note-hobby-22">[22]</a> <div class="mw-heading mw-heading3"><h3 id="Commercial_development">Commercial development</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=3" title="Edit section: Commercial development">edit</a>]</div> MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference in <a href="/wiki/Las_Vegas" title="Las Vegas">Las Vegas</a>.<a href="#cite_note-Chonacky_Winch_2005_pp._9–10-21">[21]</a><a href="#cite_note-hobby-22">[22]</a> <a href="/wiki/MathWorks" title="MathWorks">MathWorks</a>, Inc. was founded to develop the software<a href="#cite_note-Press_2008_p._6-26">[26]</a> and the MATLAB programming language was released.<a href="#cite_note-Moler_Little_pp._1–67-24">[24]</a> The first MATLAB sale was the following year, when <a href="/wiki/Nick_Trefethen" title="Nick Trefethen">Nick Trefethen</a> from the <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a> bought ten copies.<a href="#cite_note-hobby-22">[22]</a><a href="#cite_note-LoTurco_2020-29">[29]</a> By the end of the 1980s, several hundred copies of MATLAB had been sold to universities for student use.<a href="#cite_note-hobby-22">[22]</a> The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks.<a href="#cite_note-Xue_Press_2020_p._21-25">[25]</a> Many of the toolboxes were developed as a result of <a href="/wiki/Stanford_University" title="Stanford University">Stanford</a> students that used MATLAB in academia, then brought the software with them to the private sector.<a href="#cite_note-hobby-22">[22]</a> Over time, MATLAB was re-written for early operating systems created by <a href="/wiki/Digital_Equipment_Corporation" title="Digital Equipment Corporation">Digital Equipment Corporation</a>, <a href="/wiki/VAX" title="VAX">VAX</a>, <a href="/wiki/Sun_Microsystems" title="Sun Microsystems">Sun Microsystems</a>, and for Unix PCs.<a href="#cite_note-hobby-22">[22]</a><a href="#cite_note-Moler_Little_pp._1–67-24">[24]</a> Version 3 was released in 1987.<a href="#cite_note-Gatto_Rizzoli_1993_pp._85–88-30">[30]</a> The first MATLAB compiler was developed by <a href="/wiki/Stephen_C._Johnson" title="Stephen C. Johnson">Stephen C. Johnson</a> in the 1990s.<a href="#cite_note-Moler_Little_pp._1–67-24">[24]</a> In 2000, MathWorks added a Fortran-based library for linear algebra in MATLAB 6, replacing the software's original LINPACK and EISPACK subroutines that were in C.<a href="#cite_note-Moler_Little_pp._1–67-24">[24]</a> MATLAB's Parallel Computing Toolbox was released at the 2004 Supercomputing Conference and support for graphics processing units (GPUs) was added to it in 2010.<a href="#cite_note-Moler_Little_pp._1–67-24">[24]</a> <div class="mw-heading mw-heading3"><h3 id="Recent_history">Recent history</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=4" title="Edit section: Recent history">edit</a>]</div> Some especially large changes to the software were made with version 8 in 2012.<a href="#cite_note-Cho_Martinez_2014_p.-31">[31]</a> The <a href="/wiki/User_interface" title="User interface">user interface</a> was reworked[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] and <a href="/wiki/Simulink" title="Simulink">Simulink</a>'s functionality was expanded.<a href="#cite_note-Xue_Chen_2013_p._17-32">[32]</a> By 2016, MATLAB had introduced several technical and user interface improvements, including the MATLAB Live <a href="/wiki/Source-code_editor" title="Source-code editor">Editor</a> notebook, and other features.<a href="#cite_note-Moler_Little_pp._1–67-24">[24]</a> <div class="mw-heading mw-heading2"><h2 id="Release_history">Release history</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=5" title="Edit section: Release history">edit</a>]</div> For a complete list of changes of both MATLAB an official toolboxes, check MATLAB previous releases.<a href="#cite_note-33">[33]</a> <table class="sortable wikitable"> <caption>Versions of the MATLAB product family </caption> <tbody><tr> <th>Name of release </th> <th>MATLAB </th> <th>Simulink, Stateflow (MATLAB attachments) </th> <th>Year </th></tr> <tr> <th>Volume 8 </th> <td>5.0 </td> <td> </td> <td>1996 </td></tr> <tr> <th>Volume 9 </th> <td>5.1 </td> <td> </td> <td>1997 </td></tr> <tr> <th>R9.1 </th> <td>5.1.1 </td> <td> </td> <td>1997 </td></tr> <tr> <th>R10 </th> <td>5.2 </td> <td> </td> <td>1998 </td></tr> <tr> <th>R10.1 </th> <td>5.2.1 </td> <td> </td> <td>1998 </td></tr> <tr> <th>R11 </th> <td>5.3 </td> <td> </td> <td>1999 </td></tr> <tr> <th>R11.1 </th> <td>5.3.1 </td> <td> </td> <td>1999 </td></tr> <tr> <th>R12 </th> <td>6.0 </td> <td> </td> <td>2000 </td></tr> <tr> <th>R12.1 </th> <td>6.1 </td> <td> </td> <td>2001 </td></tr> <tr> <th>R13 </th> <td>6.5 </td> <td> </td> <td>2002 </td></tr> <tr> <th>R13SP1 </th> <td>6.5.1 </td> <td> </td> <td rowspan="2">2003 </td></tr> <tr> <th>R13SP2 </th> <td>6.5.2 </td> <td> </td></tr> <tr> <th>R14 </th> <td>7 </td> <td>6.0 </td> <td rowspan="2">2004 </td></tr> <tr> <th>R14SP1 </th> <td>7.0.1 </td> <td>6.1 </td></tr> <tr> <th>R14SP2 </th> <td>7.0.4 </td> <td>6.2 </td> <td rowspan="2">2005 </td></tr> <tr> <th>R14SP3 </th> <td>7.1 </td> <td>6.3 </td></tr> <tr> <th>R2006a </th> <td>7.2 </td> <td>6.4 </td> <td rowspan="2">2006 </td></tr> <tr> <th>R2006b </th> <td>7.3 </td> <td>6.5 </td></tr> <tr> <th>R2007a </th> <td>7.4 </td> <td>6.6 </td> <td rowspan="2">2007 </td></tr> <tr> <th>R2007b </th> <td>7.5 </td> <td>7.0 </td></tr> <tr> <th>R2008a </th> <td>7.6 </td> <td>7.1 </td> <td rowspan="2">2008 </td></tr> <tr> <th>R2008b </th> <td>7.7 </td> <td>7.2 </td></tr> <tr> <th>R2009a </th> <td>7.8 </td> <td>7.3 </td> <td rowspan="2">2009 </td></tr> <tr> <th>R2009b </th> <td>7.9 </td> <td>7.4 </td></tr> <tr> <th>R2010a </th> <td>7.10 </td> <td>7.5 </td> <td rowspan="2">2010 </td></tr> <tr> <th>R2010b </th> <td>7.11 </td> <td>7.6 </td></tr> <tr> <th>R2011a </th> <td>7.12 </td> <td>7.7 </td> <td rowspan="2">2011 </td></tr> <tr> <th>R2011b </th> <td>7.13 </td> <td>7.8 </td></tr> <tr> <th>R2012a </th> <td>7.14 </td> <td>7.9 </td> <td rowspan="2">2012 </td></tr> <tr> <th>R2012b </th> <td>8.0 </td> <td>8.0 </td></tr> <tr> <th>R2013a </th> <td>8.1 </td> <td>8.1 </td> <td rowspan="2">2013 </td></tr> <tr> <th>R2013b </th> <td>8.2 </td> <td>8.2 </td></tr> <tr> <th>R2014a </th> <td>8.3 </td> <td>8.3 </td> <td rowspan="2">2014 </td></tr> <tr> <th>R2014b </th> <td>8.4 </td> <td>8.4 </td></tr> <tr> <th>R2015a </th> <td>8.5 </td> <td>8.5 </td> <td rowspan="2">2015 </td></tr> <tr> <th>R2015b </th> <td>8.6 </td> <td>8.6 </td></tr> <tr> <th>R2016a </th> <td>9.0 </td> <td>8.7 </td> <td rowspan="2">2016 </td></tr> <tr> <th>R2016b </th> <td>9.1 </td> <td>8.8 </td></tr> <tr> <th>R2017a </th> <td>9.2 </td> <td>8.9 </td> <td rowspan="2">2017 </td></tr> <tr> <th>R2017b </th> <td>9.3 </td> <td>9.0 </td></tr> <tr> <th>R2018a </th> <td>9.4 </td> <td>9.1 </td> <td rowspan="2">2018 </td></tr> <tr> <th>R2018b </th> <td>9.5 </td> <td>9.2 </td></tr> <tr> <th>R2019a </th> <td>9.6 </td> <td>9.3 </td> <td rowspan="2">2019 </td></tr> <tr> <th>R2019b </th> <td>9.7 </td> <td>10.0 </td></tr> <tr> <th>R2020a </th> <td>9.8 </td> <td>10.1 </td> <td rowspan="2">2020 </td></tr> <tr> <th>R2020b </th> <td>9.9 </td> <td>10.2 </td></tr> <tr> <th>R2021a </th> <td>9.10 </td> <td>10.3 </td> <td rowspan="2">2021 </td></tr> <tr> <th>R2021b </th> <td>9.11 </td> <td>10.4 </td></tr> <tr> <th>R2022a </th> <td>9.12 </td> <td>10.5 </td> <td rowspan="2">2022 </td></tr> <tr> <th>R2022b </th> <td>9.13 </td> <td>10.6 </td></tr> <tr> <th>R2023a </th> <td>9.14 </td> <td>10.7 </td> <td rowspan="2">2023 </td></tr> <tr> <th>R2023b </th> <td>23.2 </td> <td>23.2 </td></tr> <tr> <th>R2024a </th> <td>24.1 </td> <td>24.1 </td> <td rowspan="2">2024 </td></tr> <tr> <th>R2024b </th> <td>24.2 </td> <td>24.2 </td></tr> </tbody></table> <div class="mw-heading mw-heading2"><h2 id="Syntax">Syntax</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=6" title="Edit section: Syntax">edit</a>]</div> The MATLAB application is built around the MATLAB programming language. Common usage of the MATLAB application involves using the "<a href="/wiki/Command-line_interface" title="Command-line interface">Command Window</a>" as an interactive mathematical <a href="/wiki/Command_line_interface" class="mw-redirect" title="Command line interface">shell</a> or executing <a href="/wiki/Text_file" title="Text file">text files</a> containing MATLAB code.<a href="#cite_note-34">[34]</a> <div class="mw-heading mw-heading3"><h3 id=""Hello,_world!"_example">"Hello, world!" example</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=7" title="Edit section: "Hello, world!" example">edit</a>]</div> An example of a <a href="/wiki/%22Hello,_world!%22_program" class="mw-redirect" title=""Hello, world!" program">"Hello, world!" program</a> exists in MATLAB. <div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>disp('Hello, world!') </pre></div> It displays like so: <div class="mw-highlight mw-highlight-lang-output mw-content-ltr" dir="ltr"><pre>Hello, world! </pre></div> <div class="mw-heading mw-heading3"><h3 id="Variables">Variables</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=8" title="Edit section: Variables">edit</a>]</div> <a href="/wiki/Variable_(computer_science)" title="Variable (computer science)">Variables</a> are defined using the <a href="/wiki/Assignment_(computer_science)" title="Assignment (computer science)">assignment</a> operator, <code>=</code>. MATLAB is a <a href="/wiki/Strong_and_weak_typing" title="Strong and weak typing">weakly typed</a> programming language because <a href="/wiki/Data_type" title="Data type">types</a> are implicitly converted.<a href="#cite_note-35">[35]</a> It is an <a href="/wiki/Type_inference" title="Type inference">inferred</a> <a href="/wiki/Type_system" title="Type system">typed language</a> because variables can be assigned without declaring their type, except if they are to be treated as symbolic objects,<a href="#cite_note-36">[36]</a> and that their type can change. Values can come from <a href="/wiki/Constant_(computer_science)" class="mw-redirect" title="Constant (computer science)">constants</a>, from computation involving values of other variables, or from the output of a <a href="/wiki/Function_(computer_programming)" title="Function (computer programming)">function</a>. For example: <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> x = 17 x = 17 >> x = 'hat' x = hat >> x = [3*4, pi/2] x = 12.0000 1.5708 >> y = 3*sin(x) y = -1.6097 3.0000 </pre></div> <div class="mw-heading mw-heading3"><h3 id="Vectors_and_matrices">Vectors and matrices</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=9" title="Edit section: Vectors and matrices">edit</a>]</div> A simple array is defined using the colon syntax: initial<code>:</code>increment<code>:</code>terminator. For instance: <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> array = 1:2:9 array = 1 3 5 7 9 </pre></div> defines a variable named <code>array</code> (or assigns a new value to an existing variable with the name <code>array</code>) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the initial value), increments with each step from the previous value by 2 (the increment value), and stops once it reaches (or is about to exceed) 9 (the terminator value). The increment value can actually be left out of this syntax (along with one of the colons), to use a default value of 1. <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> ari = 1:5 ari = 1 2 3 4 5 </pre></div> assigns to the variable named <code>ari</code> an array with the values 1, 2, 3, 4, and 5, since the default value of 1 is used as the increment. <a href="/wiki/One-based_indexing" class="mw-redirect" title="One-based indexing">Indexing</a> is one-based,<a href="#cite_note-37">[37]</a> which is the usual convention for <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrices</a> in mathematics, unlike zero-based indexing commonly used in other programming languages such as C, <a href="/wiki/C%2B%2B" title="C++">C++</a>, and <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a>. Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to separate the rows. The list of elements should be surrounded by square brackets <code>[]</code>. Parentheses <code>()</code> are used to access elements and subarrays (they are also used to denote a function argument list). <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> A = [16, 3, 2, 13 ; 5, 10, 11, 8 ; 9, 6, 7, 12 ; 4, 15, 14, 1] A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 >> A(2,3) ans = 11 </pre></div> Sets of indices can be specified by expressions such as <code>2:4</code>, which evaluates to <code>[2, 3, 4]</code>. For example, a submatrix taken from rows 2 through 4 and columns 3 through 4 can be written as: <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> A(2:4,3:4) ans = 11 8 7 12 14 1 </pre></div> A square <a href="/wiki/Identity_matrix" title="Identity matrix">identity matrix</a> of size n can be generated using the function <code>eye</code>, and matrices of any size with zeros or ones can be generated with the functions <code>zeros</code> and <code>ones</code>, respectively. <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> eye(3,3) ans = 1 0 0 0 1 0 0 0 1 >> zeros(2,3) ans = 0 0 0 0 0 0 >> ones(2,3) ans = 1 1 1 1 1 1 </pre></div> <a href="/wiki/Transpose" title="Transpose">Transposing</a> a vector or a matrix is done either by the function <code>transpose</code> or by adding dot-prime after the matrix (without the dot, prime will perform <a href="/wiki/Conjugate_transpose" title="Conjugate transpose">conjugate transpose</a> for complex arrays): <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> A = [1 ; 2], B = A.', C = transpose(A) A = 1 2 B = 1 2 C = 1 2 >> D = [0, 3 ; 1, 5], D.' D = 0 3 1 5 ans = 0 1 3 5 </pre></div> Most functions accept arrays as input and operate element-wise on each element. For example, <code>mod(2*J,n)</code> will multiply every element in J by 2, and then reduce each element modulo n. MATLAB does include standard <code>for</code> and <code>while</code> loops, but (as in other similar applications such as <a href="/wiki/APL_(programming_language)" title="APL (programming language)">APL</a> and <a href="/wiki/R_(programming_language)" title="R (programming language)">R</a>), using the <a href="/wiki/Array_programming" title="Array programming">vectorized</a> notation is encouraged and is often faster to execute. The following code, excerpted from the function magic.m, creates a <a href="/wiki/Magic_square" title="Magic square">magic square</a> M for odd values of n (MATLAB function <code>meshgrid</code> is used here to generate square matrices I and J containing ⁠<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1:n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>:</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1:n}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b62854651e7b5b8766d9b089edce5ed4f3379fa4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.494ex; height:2.176ex;" alt="{\displaystyle 1:n}" />⁠): <div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>[J,I] = meshgrid(1:n); A = mod(I + J - (n + 3) / 2, n); B = mod(I + 2 * J - 2, n); M = n * A + B + 1; </pre></div> <div class="mw-heading mw-heading3"><h3 id="Structures">Structures</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=10" title="Edit section: Structures">edit</a>]</div> MATLAB supports structure data types.<a href="#cite_note-38">[38]</a> Since all variables in MATLAB are arrays, a more adequate name is "structure array", where each element of the array has the same field names. In addition, MATLAB supports dynamic field names<a href="#cite_note-39">[39]</a> (field look-ups by name, field manipulations, etc.). <div class="mw-heading mw-heading3"><h3 id="Functions">Functions</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=11" title="Edit section: Functions">edit</a>]</div> When creating a MATLAB function, the name of the file should match the name of the first function in the file. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores. Variables and functions are case sensitive.<a href="#cite_note-40">[40]</a> <div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>rgbImage = imread('ecg.png'); grayImage = rgb2gray(rgbImage); % for non-indexed images level = graythresh(grayImage); % threshold for converting image to binary, binaryImage = im2bw(grayImage, level); % Extract the individual red, green, and blue color channels. redChannel = rgbImage(:, :, 1); greenChannel = rgbImage(:, :, 2); blueChannel = rgbImage(:, :, 3); % Make the black parts pure red. redChannel(~binaryImage) = 255; greenChannel(~binaryImage) = 0; blueChannel(~binaryImage) = 0; % Now recombine to form the output image. rgbImageOut = cat(3, redChannel, greenChannel, blueChannel); imshow(rgbImageOut); </pre></div> <div class="mw-heading mw-heading3"><h3 id="Function_handles">Function handles</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=12" title="Edit section: Function handles">edit</a>]</div> MATLAB supports elements of <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a> by introducing function handles,<a href="#cite_note-41">[41]</a> or function references, which are implemented either in .m files or anonymous<a href="#cite_note-42">[42]</a>/nested functions.<a href="#cite_note-43">[43]</a> <div class="mw-heading mw-heading3"><h3 id="Classes_and_object-oriented_programming">Classes and object-oriented programming</h3>[<a href="/w/index.php?title=MATLAB&action=edit&section=13" title="Edit section: Classes and object-oriented programming">edit</a>]</div> MATLAB supports <a href="/wiki/Object-oriented_programming" title="Object-oriented programming">object-oriented programming</a> including classes, <a href="/wiki/Inheritance_(object-oriented_programming)" title="Inheritance (object-oriented programming)">inheritance</a>, virtual dispatch, packages, <a href="/wiki/Pass-by-value" class="mw-redirect" title="Pass-by-value">pass-by-value</a> semantics, and <a href="/wiki/Pass-by-reference" class="mw-redirect" title="Pass-by-reference">pass-by-reference</a> semantics.<a href="#cite_note-44">[44]</a> However, the syntax and calling conventions are significantly different from other languages. MATLAB has value classes and reference classes, depending on whether the class has handle as a super-class (for reference classes) or not (for value classes).<a href="#cite_note-45">[45]</a> Method call behavior is different between value and reference classes. For example, a call to a method: <div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>object.method(); </pre></div> can alter any member of object only if object is an instance of a reference class, otherwise value class methods must return a new instance if it needs to modify the object. An example of a simple class is provided below: <div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>classdef Hello methods function greet(obj) disp('Hello!') end end end </pre></div> When put into a file named <code>hello.m</code>, this can be executed with the following commands: <div class="mw-highlight mw-highlight-lang-matlabsession mw-content-ltr" dir="ltr"><pre>>> x = Hello(); >> x.greet(); Hello! </pre></div> <div class="mw-heading mw-heading2"><h2 id="Graphics_and_graphical_user_interface_programming">Graphics and graphical user interface programming</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=14" title="Edit section: Graphics and graphical user interface programming">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Notice plainlinks metadata ambox ambox-notice" role="presentation" style="width:100%;margin:0;"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/1/1d/Information_icon4.svg/40px-Information_icon4.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/1/1d/Information_icon4.svg/60px-Information_icon4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/1/1d/Information_icon4.svg/80px-Information_icon4.svg.png 2x" data-file-width="620" data-file-height="620" /></div></td><td class="mbox-text" style="text-align: left;"><div class="mbox-text-span">Graphs are unavailable due to technical issues. Updates on reimplementing the Graph extension, which will be known as the Chart extension, can be found on <a class="external text" href="https://phabricator.wikimedia.org/tag/charts/">Phabricator</a> and on <a href="https://www.mediawiki.org/wiki/Extension:Chart" class="extiw" title="mw:Extension:Chart">MediaWiki.org</a>.</div></td></tr></tbody></table> MATLAB has tightly integrated graph-plotting features. For example, the function plot can be used to produce a graph from two vectors x and y. The code: <div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>x = 0:pi/100:2*pi; y = sin(x); plot(x,y) </pre></div> produces the following figure of the <a href="/wiki/Sine_wave" title="Sine wave">sine function</a>: <a href="/wiki/File:Matlab_plot_sin.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Matlab_plot_sin.svg/500px-Matlab_plot_sin.svg.png" decoding="async" width="350" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Matlab_plot_sin.svg/960px-Matlab_plot_sin.svg.png 1.5x" data-file-width="1052" data-file-height="744" /></a> MATLAB supports three-dimensional graphics as well: <table> <tbody><tr> <td valign="top"><div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>[X,Y] = meshgrid(-10:0.25:10,-10:0.25:10); f = sinc(sqrt((X/pi).^2+(Y/pi).^2)); mesh(X,Y,f); axis([-10 10 -10 10 -0.3 1]) xlabel('{\bfx}') ylabel('{\bfy}') zlabel('{\bfsinc} ({\bfR})') hidden off </pre></div> </td> <td>    </td> <td valign="top"><div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>[X,Y] = meshgrid(-10:0.25:10,-10:0.25:10); f = sinc(sqrt((X/pi).^2+(Y/pi).^2)); surf(X,Y,f); axis([-10 10 -10 10 -0.3 1]) xlabel('{\bfx}') ylabel('{\bfy}') zlabel('{\bfsinc} ({\bfR})') </pre></div> </td></tr> <tr> <td>This code produces a <a href="/wiki/Wire_frame_model" class="mw-redirect" title="Wire frame model">wireframe</a> 3D plot of the two-dimensional unnormalized <a href="/wiki/Sinc_function" title="Sinc function">sinc function</a>: </td> <td>    </td> <td>This code produces a surface 3D plot of the two-dimensional unnormalized <a href="/wiki/Sinc_function" title="Sinc function">sinc function</a>: </td></tr> <tr> <td style="text-align:center;"><a href="/wiki/File:MATLAB_mesh_sinc3D.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/MATLAB_mesh_sinc3D.svg/512px-MATLAB_mesh_sinc3D.svg.png" decoding="async" width="512" height="384" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/MATLAB_mesh_sinc3D.svg/768px-MATLAB_mesh_sinc3D.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/MATLAB_mesh_sinc3D.svg/1024px-MATLAB_mesh_sinc3D.svg.png 2x" data-file-width="512" data-file-height="384" /></a> </td> <td>    </td> <td style="text-align:center;"><a href="/wiki/File:MATLAB_surf_sinc3D.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/MATLAB_surf_sinc3D.svg/512px-MATLAB_surf_sinc3D.svg.png" decoding="async" width="512" height="384" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/MATLAB_surf_sinc3D.svg/768px-MATLAB_surf_sinc3D.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/MATLAB_surf_sinc3D.svg/1024px-MATLAB_surf_sinc3D.svg.png 2x" data-file-width="512" data-file-height="384" /></a> </td></tr></tbody></table> MATLAB supports developing <a href="/wiki/Graphical_user_interface" title="Graphical user interface">graphical user interface</a> (GUI) applications.<a href="#cite_note-46">[46]</a> UIs can be generated either programmatically or using visual design environments such as GUIDE and App Designer.<a href="#cite_note-47">[47]</a><a href="#cite_note-48">[48]</a> <div class="mw-heading mw-heading2"><h2 id="MATLAB_and_other_languages">MATLAB and other languages</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=15" title="Edit section: MATLAB and other languages">edit</a>]</div> MATLAB can call functions and subroutines written in the programming languages <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> or <a href="/wiki/Fortran" title="Fortran">Fortran</a>.<a href="#cite_note-49">[49]</a> A wrapper function is created allowing MATLAB data types to be passed and returned. <a href="/wiki/MEX_file" title="MEX file">MEX files</a> (MATLAB executables) are the dynamically loadable object files created by compiling such functions.<a href="#cite_note-50">[50]</a><a href="#cite_note-51">[51]</a> Since 2014 increasing two-way interfacing with <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> was being added.<a href="#cite_note-52">[52]</a><a href="#cite_note-53">[53]</a> Libraries written in <a href="/wiki/Perl" title="Perl">Perl</a>, <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a>, <a href="/wiki/ActiveX" title="ActiveX">ActiveX</a> or <a href="/wiki/.NET_Framework" title=".NET Framework">.NET</a> can be directly called from MATLAB,<a href="#cite_note-54">[54]</a><a href="#cite_note-55">[55]</a> and many MATLAB libraries (for example <a href="/wiki/XML" title="XML">XML</a> or <a href="/wiki/SQL" title="SQL">SQL</a> support) are implemented as wrappers around Java or ActiveX libraries. Calling MATLAB from Java is more complicated, but can be done with a MATLAB toolbox<a href="#cite_note-56">[56]</a> which is sold separately by <a href="/wiki/MathWorks" title="MathWorks">MathWorks</a>, or using an undocumented mechanism called JMI (Java-to-MATLAB Interface),<a href="#cite_note-57">[57]</a><a href="#cite_note-58">[58]</a> (which should not be confused with the unrelated <a href="/wiki/Java_Metadata_Interface" title="Java Metadata Interface">Java Metadata Interface</a> that is also called JMI). Official MATLAB API for Java was added in 2016.<a href="#cite_note-MATLAB_Engine_API_for_Java-59">[59]</a> As alternatives to the <a href="/wiki/MuPAD" title="MuPAD">MuPAD</a> based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to <a href="/wiki/Maple_(software)" title="Maple (software)">Maple</a> or <a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a>.<a href="#cite_note-60">[60]</a><a href="#cite_note-61">[61]</a> Libraries also exist to import and export <a href="/wiki/MathML" title="MathML">MathML</a>.<a href="#cite_note-62">[62]</a> <div class="mw-heading mw-heading2"><h2 id="Relations_to_US_sanctions">Relations to US sanctions</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=16" title="Edit section: Relations to US sanctions">edit</a>]</div> In 2020, MATLAB withdrew services from two Chinese universities as a result of US sanctions. The universities said this will be responded to by increased use of open-source alternatives and by developing domestic alternatives.<a href="#cite_note-63">[63]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=17" title="Edit section: See also">edit</a>]</div> <ul><li><a href="/wiki/Comparison_of_numerical-analysis_software" title="Comparison of numerical-analysis software">Comparison of numerical-analysis software</a></li> <li><a href="/wiki/List_of_numerical-analysis_software" title="List of numerical-analysis software">List of numerical-analysis software</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=18" title="Edit section: Notes">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.mathworks.com/company/newsletters/articles/the-l-shaped-membrane.html">"The L-Shaped Membrane"</a>. 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MathWorks. Retrieved September 15, 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=MATLAB+Engine+API+for+Java&rft.pub=MathWorks&rft_id=http%3A%2F%2Fwww.mathworks.com%2Fhelp%2Fmatlab%2Fmatlab-engine-api-for-java.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"> </li> <li id="cite_note-60"><a href="#cite_ref-60">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGermundsson1998" class="citation web cs1">Germundsson, Roger (September 30, 1998). <a rel="nofollow" class="external text" href="http://library.wolfram.com/infocenter/MathSource/618/">"MaMa: Calling MATLAB from Mathematica with MathLink"</a>. <a href="/wiki/Wolfram_Research" title="Wolfram Research">Wolfram Research</a>. Wolfram Library Archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Wolfram+Research&rft.atitle=MaMa%3A+Calling+MATLAB+from+Mathematica+with+MathLink&rft.date=1998-09-30&rft.aulast=Germundsson&rft.aufirst=Roger&rft_id=http%3A%2F%2Flibrary.wolfram.com%2Finfocenter%2FMathSource%2F618%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"> </li> <li id="cite_note-61"><a href="#cite_ref-61">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFrsmenonszhorvat2013" class="citation web cs1">rsmenon; szhorvat (2013). <a rel="nofollow" class="external text" href="http://matlink.org/">"MATLink: Communicate with MATLAB from Mathematica"</a>. 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Retrieved August 14, 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=MathML+import%2Fexport&rft.pub=MathWorks+-+File+Exchange&rft.date=2006-09-01&rft.aulast=Weitzel&rft.aufirst=Michael&rft_id=http%3A%2F%2Fwww.mathworks.com%2Fmatlabcentral%2Ffileexchange%2F7709-mathml-importexport&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"> </li> <li id="cite_note-63"><a href="#cite_ref-63">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.scmp.com/news/china/diplomacy/article/3088854/us-military-ban-locks-two-chinese-universities-out-popular">"US military ban locks two Chinese universities out of popular software"</a>. South China Morning Post. June 12, 2020. Retrieved November 6, 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=South+China+Morning+Post&rft.atitle=US+military+ban+locks+two+Chinese+universities+out+of+popular+software&rft.date=2020-06-12&rft_id=https%3A%2F%2Fwww.scmp.com%2Fnews%2Fchina%2Fdiplomacy%2Farticle%2F3088854%2Fus-military-ban-locks-two-chinese-universities-out-popular&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=19" title="Edit section: Further reading">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1">Gilat, Amos (2004). MATLAB: An Introduction with Applications 2nd Edition. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-69420-5" title="Special:BookSources/978-0-471-69420-5"><bdi>978-0-471-69420-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=MATLAB%3A+An+Introduction+with+Applications+2nd+Edition&rft.pub=John+Wiley+%26+Sons&rft.date=2004&rft.isbn=978-0-471-69420-5&rft.aulast=Gilat&rft.aufirst=Amos&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1"><a href="/wiki/Alfio_Quarteroni" title="Alfio Quarteroni">Quarteroni, Alfio</a>; Saleri, Fausto (2006). Scientific Computing with MATLAB and Octave. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-32612-0" title="Special:BookSources/978-3-540-32612-0"><bdi>978-3-540-32612-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Scientific+Computing+with+MATLAB+and+Octave&rft.pub=Springer&rft.date=2006&rft.isbn=978-3-540-32612-0&rft.aulast=Quarteroni&rft.aufirst=Alfio&rft.au=Saleri%2C+Fausto&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1">Ferreira, A.J.M. (2009). MATLAB Codes for Finite Element Analysis. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-9199-5" title="Special:BookSources/978-1-4020-9199-5"><bdi>978-1-4020-9199-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=MATLAB+Codes+for+Finite+Element+Analysis&rft.pub=Springer&rft.date=2009&rft.isbn=978-1-4020-9199-5&rft.aulast=Ferreira&rft.aufirst=A.J.M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1">Lynch, Stephen (2004). Dynamical Systems with Applications using MATLAB. Birkhäuser. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8176-4321-8" title="Special:BookSources/978-0-8176-4321-8"><bdi>978-0-8176-4321-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dynamical+Systems+with+Applications+using+MATLAB&rft.pub=Birkh%C3%A4user&rft.date=2004&rft.isbn=978-0-8176-4321-8&rft.aulast=Lynch&rft.aufirst=Stephen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMATLAB" class="Z3988"></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=MATLAB&action=edit&section=20" title="Edit section: External links">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid 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style="width:1%">Free</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Advanced_Simulation_Library" title="Advanced Simulation Library">Advanced Simulation Library</a></li> <li><a href="/wiki/ADMB" title="ADMB">ADMB</a></li> <li><a href="/wiki/Chapel_(programming_language)" title="Chapel (programming language)">Chapel</a></li> <li><a href="/wiki/Euler_Mathematical_Toolbox" title="Euler Mathematical Toolbox">Euler Mathematical Toolbox</a></li> <li><a href="/wiki/FreeFem%2B%2B" title="FreeFem++">FreeFem++</a></li> <li><a href="/wiki/FreeMat" title="FreeMat">FreeMat</a></li> <li><a href="/wiki/Genius_(mathematics_software)" title="Genius (mathematics software)">Genius</a></li> <li><a href="/wiki/Gmsh" title="Gmsh">Gmsh</a></li> <li><a href="/wiki/GNU_Octave" title="GNU Octave">GNU Octave</a></li> <li><a href="/wiki/Gretl" title="Gretl">gretl</a></li> <li><a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a></li> <li><a href="/wiki/Project_Jupyter" title="Project Jupyter">Jupyter</a> (Julia, Python, R; <a href="/wiki/IPython" title="IPython">IPython</a>)</li> <li><a href="/wiki/MFEM" title="MFEM">MFEM</a></li> <li><a href="/wiki/OpenFOAM" title="OpenFOAM">OpenFOAM</a></li> <li><a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a></li> <li><a href="/wiki/R_(programming_language)" title="R (programming language)">R</a></li> <li><a href="/wiki/SageMath" title="SageMath">SageMath</a></li> <li><a href="/wiki/Salome_(software)" title="Salome (software)">Salome</a></li> <li><a href="/wiki/ScicosLab" title="ScicosLab">ScicosLab</a></li> <li><a href="/wiki/Scilab" title="Scilab">Scilab</a></li> <li><a href="/wiki/X10_(programming_language)" title="X10 (programming language)">X10</a></li> <li><a href="/wiki/Weka_(software)" title="Weka (software)">Weka</a></li></ul> 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href="/wiki/Maple_(software)" title="Maple (software)">Maple</a></li> <li><a href="/wiki/Mathcad" title="Mathcad">Mathcad</a></li> <li><a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Mathematica</a></li> <li><a class="mw-selflink selflink">MATLAB</a></li> <li><a href="/wiki/Speakeasy_(computational_environment)" title="Speakeasy (computational environment)">Speakeasy</a></li> <li><a href="/wiki/VisSim" title="VisSim">VisSim</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div> <ul><li><a href="/wiki/Comparison_of_numerical-analysis_software" title="Comparison of numerical-analysis software">Comparison</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Computer_algebra_systems377" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computer_algebra_systems" title="Template:Computer algebra systems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Computer_algebra_systems" title="Template talk:Computer algebra systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computer_algebra_systems" title="Special:EditPage/Template:Computer algebra systems"><abbr title="Edit this template">e</abbr></a></li></ul></div><div 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title="Proprietary software">Proprietary</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Casio_ClassPad_300" title="Casio ClassPad 300">ClassPad Manager</a></li> <li><a href="/wiki/KANT_(software)" title="KANT (software)">KANT</a></li> <li><a href="/wiki/Magma_(computer_algebra_system)" title="Magma (computer algebra system)">Magma</a></li> <li><a href="/wiki/Maple_(software)" title="Maple (software)">Maple</a></li> <li><a href="/wiki/Mathcad" title="Mathcad">Mathcad</a></li> <li><a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Mathematica</a></li> <li><a href="/wiki/MuPAD" title="MuPAD">muPAD</a> (<a class="mw-selflink selflink">MATLAB</a> symbolic math toolbox)</li> <li><a href="/wiki/SMath_Studio" title="SMath Studio">SMath Studio</a></li> <li><a href="/wiki/TI_InterActive!" title="TI InterActive!">TI InterActive!</a></li> <li><a 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data-file-height="185" /><a href="/wiki/List_of_computer_algebra_systems" title="List of computer algebra systems">List</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Statistical_software284" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Statistical_software" title="Template:Statistical 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Info">Epi Info</a></li> <li><a href="/wiki/CSPro" title="CSPro">CSPro</a></li> <li><a href="/wiki/X-12-ARIMA" class="mw-redirect" title="X-12-ARIMA">X-12-ARIMA</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Open-source_software" title="Open-source software">Open-source</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ADMB" title="ADMB">ADMB</a></li> <li><a href="/wiki/DAP_(software)" title="DAP (software)">DAP</a></li> <li><a href="/wiki/Gretl" title="Gretl">gretl</a></li> <li><a href="/wiki/Jamovi" title="Jamovi">jamovi</a></li> <li><a href="/wiki/JASP" title="JASP">JASP</a></li> <li><a href="/wiki/Just_another_Gibbs_sampler" title="Just another Gibbs sampler">JAGS</a></li> <li><a href="/wiki/JMulTi" title="JMulTi">JMulTi</a></li> <li><a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a></li> <li><a href="/wiki/Project_Jupyter" title="Project Jupyter">Jupyter</a> (Julia, Python, R)</li> <li><a href="/wiki/GNU_Octave" title="GNU Octave">GNU Octave</a></li> <li><a href="/wiki/OpenBUGS" title="OpenBUGS">OpenBUGS</a></li> <li><a href="/wiki/Orange_(software)" title="Orange (software)">Orange</a></li> <li><a href="/wiki/PSPP" title="PSPP">PSPP</a></li> <li><a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> (statsmodels, <a href="/wiki/PyMC3" class="mw-redirect" title="PyMC3">PyMC3</a>, <a href="/wiki/IPython" title="IPython">IPython</a>, <a href="/wiki/IDLE" title="IDLE">IDLE</a>)</li> <li><a href="/wiki/R_(programming_language)" title="R (programming language)">R</a> (<a href="/wiki/RStudio" title="RStudio">RStudio</a>)</li> <li><a href="/wiki/SageMath" title="SageMath">SageMath</a></li> <li><a href="/wiki/SimFiT" title="SimFiT">SimFiT</a></li> <li><a href="/wiki/SOFA_Statistics" title="SOFA Statistics">SOFA Statistics</a></li> <li><a href="/wiki/Stan_(software)" title="Stan (software)">Stan</a></li> <li><a href="/wiki/XLispStat" title="XLispStat">XLispStat</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Freeware" title="Freeware">Freeware</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BV4.1_(software)" title="BV4.1 (software)">BV4.1</a></li> <li><a href="/wiki/CumFreq" title="CumFreq">CumFreq</a></li> <li><a href="/wiki/SegReg" title="SegReg">SegReg</a></li> <li><a href="/wiki/XploRe" title="XploRe">XploRe</a></li> <li><a href="/wiki/WinBUGS" title="WinBUGS">WinBUGS</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Commercial_software" title="Commercial software">Commercial</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Cross-platform_software" title="Cross-platform software">Cross-platform</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Data_Desk" title="Data Desk">Data Desk</a></li> <li><a href="/wiki/GAUSS_(software)" title="GAUSS (software)">GAUSS</a></li> <li><a href="/wiki/GraphPad_InStat" class="mw-redirect" title="GraphPad InStat">GraphPad InStat</a></li> <li><a href="/wiki/GraphPad_Prism" class="mw-redirect" title="GraphPad Prism">GraphPad Prism</a></li> <li>IBM <a href="/wiki/SPSS" title="SPSS">SPSS</a> Statistics</li> <li>IBM <a href="/wiki/SPSS_Modeler" title="SPSS Modeler">SPSS Modeler</a></li> <li><a href="/wiki/JMP_(statistical_software)" title="JMP (statistical software)">JMP</a></li> <li><a href="/wiki/Maple_(software)" title="Maple (software)">Maple</a></li> <li><a href="/wiki/Mathcad" title="Mathcad">Mathcad</a></li> <li><a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Mathematica</a></li> <li><a class="mw-selflink selflink">MATLAB</a></li> <li><a href="/wiki/OxMetrics" title="OxMetrics">OxMetrics</a></li> <li><a href="/wiki/RATS_(software)" title="RATS (software)">RATS</a></li> <li><a href="/wiki/Revolution_Analytics" title="Revolution Analytics">Revolution Analytics</a></li> <li><a href="/wiki/SAS_(software)" title="SAS (software)">SAS</a></li> <li><a href="/wiki/SmartPLS" title="SmartPLS">SmartPLS</a></li> <li><a href="/wiki/Stata" title="Stata">Stata</a></li> <li><a href="/wiki/StatView" title="StatView">StatView</a></li> <li><a href="/wiki/SUDAAN" title="SUDAAN">SUDAAN</a></li> <li><a href="/wiki/S-PLUS" title="S-PLUS">S-PLUS</a></li> <li><a href="/wiki/TSP_(econometrics_software)" title="TSP (econometrics software)">TSP</a></li> <li><a href="/wiki/World_Programming_System" title="World Programming System">World Programming System</a> (WPS)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Microsoft_Windows" title="Microsoft Windows">Windows</a> only</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BMDP" title="BMDP">BMDP</a></li> <li><a href="/wiki/EViews" title="EViews">EViews</a></li> <li><a href="/wiki/Genstat" title="Genstat">GenStat</a></li> <li><a href="/wiki/LIMDEP" title="LIMDEP">LIMDEP</a></li> <li><a href="/wiki/LISREL" title="LISREL">LISREL</a></li> <li><a href="/wiki/MedCalc" title="MedCalc">MedCalc</a></li> <li><a href="/wiki/Microfit" title="Microfit">Microfit</a></li> <li><a href="/wiki/Minitab" title="Minitab">Minitab</a></li> <li><a href="/wiki/MLwiN" title="MLwiN">MLwiN</a></li> <li><a href="/wiki/NCSS_(statistical_software)" title="NCSS (statistical software)">NCSS</a></li> <li><a href="/wiki/Shazam_(econometrics_software)" title="Shazam (econometrics software)">Shazam</a></li> <li><a href="/wiki/SigmaStat" title="SigmaStat">SigmaStat</a></li> <li><a href="/wiki/Statistica" title="Statistica">Statistica</a></li> <li><a href="/wiki/StatsDirect" title="StatsDirect">StatsDirect</a></li> <li><a href="/wiki/StatXact" title="StatXact">StatXact</a></li> <li><a href="/wiki/SYSTAT_(statistics_package)" title="SYSTAT (statistics package)">SYSTAT</a></li> <li><a href="/wiki/The_Unscrambler" title="The Unscrambler">The Unscrambler</a></li> <li>Unistat</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Microsoft_Excel" title="Microsoft Excel">Excel</a> add-ons</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analyse-it" title="Analyse-it">Analyse-it</a></li> <li>Unistat for Excel</li> <li><a href="/wiki/XLfit" title="XLfit">XLfit</a></li> <li><a href="/wiki/RExcel" title="RExcel">RExcel</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/Comparison_of_statistical_packages" title="Comparison of statistical packages">Comparison</a> • <a href="/wiki/Category:Statistical_software" title="Category:Statistical software">Category</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Image_processing_software87" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Image_processing_software" title="Template:Image processing software"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Image_processing_software" title="Template talk:Image processing software"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Image_processing_software" title="Special:EditPage/Template:Image processing software"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Image_processing_software87" style="font-size:114%;margin:0 4em"><a href="/wiki/Image_processing" class="mw-redirect" title="Image processing">Image processing</a> software</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Free_software" title="Free software">Free</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/3D_Slicer" title="3D Slicer">3D Slicer</a></li> <li><a href="/wiki/Analysis_of_Functional_NeuroImages" title="Analysis of Functional NeuroImages">AFNI</a></li> <li><a href="/wiki/CellCognition" title="CellCognition">CellCognition</a></li> <li><a href="/wiki/CellProfiler" title="CellProfiler">CellProfiler</a></li> <li><a href="/wiki/Dlib" title="Dlib">Dlib</a></li> <li><a href="/wiki/Endrov" title="Endrov">Endrov</a></li> <li><a href="/wiki/Fiji_(software)" title="Fiji (software)">Fiji</a></li> <li><a href="/wiki/FMRIB_Software_Library" title="FMRIB Software Library">FMRIB Software Library</a></li> <li><a href="/wiki/FreeSurfer" title="FreeSurfer">FreeSurfer</a></li> <li><a href="/wiki/GemIdent" title="GemIdent">GemIdent</a></li> <li><a href="/wiki/GNU_Octave" title="GNU Octave">GNU Octave</a></li> <li><a href="/wiki/Ilastik" title="Ilastik">ilastik</a></li> <li><a href="/wiki/ImageJ" title="ImageJ">ImageJ</a></li> <li><a href="/wiki/IMOD_(software)" title="IMOD (software)">IMOD</a></li> <li><a href="/wiki/Insight_Segmentation_and_Registration_Toolkit" title="Insight Segmentation and Registration Toolkit">ITK</a></li> <li><a href="/wiki/InVesalius" title="InVesalius">InVesalius</a></li> <li><a href="/wiki/ITK-SNAP" title="ITK-SNAP">ITK-SNAP</a></li> <li><a href="/wiki/KNIME" title="KNIME">KNIME</a></li> <li><a href="/wiki/Mango_(software)" title="Mango (software)">Mango</a></li> <li><a href="/wiki/OpenCV" title="OpenCV">OpenCV</a></li> <li><a href="/wiki/OsiriX" title="OsiriX">OsiriX</a></li> <li><a href="/wiki/VIGRA" title="VIGRA">VIGRA</a></li> <li><a href="/wiki/VXL" title="VXL">VXL</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proprietary_software" title="Proprietary software">Proprietary</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amira_(software)" title="Amira (software)">Amira</a></li> <li><a href="/wiki/Analyze_(imaging_software)" title="Analyze (imaging software)">Analyze</a></li> <li><a href="/wiki/Aphelion_(software)" title="Aphelion (software)">Aphelion</a></li> <li><a href="/wiki/Avizo_(software)" title="Avizo (software)">Avizo</a></li> <li><a href="/wiki/Bitplane" title="Bitplane">Bitplane</a></li> <li><a href="/wiki/IDL_(programming_language)" title="IDL (programming language)">IDL</a></li></ul> <ul><li><a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Mathematica</a></li> <li><a class="mw-selflink selflink">MATLAB</a></li> <li><a href="/wiki/Materialise_Mimics" title="Materialise Mimics">Mimics</a></li> <li><a href="/wiki/MountainsMap" title="MountainsMap">MountainsMap</a></li> <li><a href="/wiki/Tomviz" title="Tomviz">Tomviz</a></li> <li><a href="/wiki/Visage_SDK" title="Visage SDK">Visage SDK</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Linear_algebra379" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Linear_algebra" title="Template:Linear algebra"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Linear_algebra" title="Template talk:Linear algebra"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Linear_algebra" title="Special:EditPage/Template:Linear algebra"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Linear_algebra379" style="font-size:114%;margin:0 4em"><a href="/wiki/Linear_algebra" title="Linear algebra">Linear algebra</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><a href="/wiki/Outline_of_linear_algebra" title="Outline of linear algebra">Outline</a></li> <li><a href="/wiki/Glossary_of_linear_algebra" title="Glossary of linear algebra">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basic concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Scalar_(mathematics)" title="Scalar (mathematics)">Scalar</a></li> <li><a href="/wiki/Euclidean_vector" title="Euclidean vector">Vector</a></li> <li><a href="/wiki/Vector_space" title="Vector space">Vector space</a></li> <li><a href="/wiki/Scalar_multiplication" title="Scalar multiplication">Scalar multiplication</a></li> <li><a href="/wiki/Vector_projection" title="Vector projection">Vector projection</a></li> <li><a href="/wiki/Linear_span" title="Linear span">Linear span</a></li> <li><a href="/wiki/Linear_map" title="Linear map">Linear map</a></li> <li><a href="/wiki/Projection_(linear_algebra)" title="Projection (linear algebra)">Linear projection</a></li> <li><a href="/wiki/Linear_independence" title="Linear independence">Linear independence</a></li> <li><a href="/wiki/Linear_combination" title="Linear combination">Linear combination</a></li> <li><a href="/wiki/Multilinear_map" title="Multilinear map">Multilinear map</a></li> <li><a href="/wiki/Basis_(linear_algebra)" title="Basis (linear algebra)">Basis</a></li> <li><a href="/wiki/Change_of_basis" title="Change of basis">Change of basis</a></li> <li><a href="/wiki/Row_and_column_vectors" title="Row and column vectors">Row and column vectors</a></li> <li><a href="/wiki/Row_and_column_spaces" title="Row and column spaces">Row and column spaces</a></li> <li><a href="/wiki/Kernel_(linear_algebra)" title="Kernel (linear algebra)">Kernel</a></li> <li><a href="/wiki/Eigenvalues_and_eigenvectors" title="Eigenvalues and eigenvectors">Eigenvalues and eigenvectors</a></li> <li><a href="/wiki/Transpose" title="Transpose">Transpose</a></li> <li><a href="/wiki/System_of_linear_equations" title="System of linear equations">Linear equations</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><a href="/wiki/Euclidean_space" title="Euclidean space"><img alt="Three dimensional Euclidean space" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Linear_subspaces_with_shading.svg/80px-Linear_subspaces_with_shading.svg.png" decoding="async" width="80" height="58" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Linear_subspaces_with_shading.svg/120px-Linear_subspaces_with_shading.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Linear_subspaces_with_shading.svg/160px-Linear_subspaces_with_shading.svg.png 2x" data-file-width="325" data-file-height="236" /></a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">Matrices</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Block_matrix" title="Block matrix">Block</a></li> <li><a href="/wiki/Matrix_decomposition" title="Matrix decomposition">Decomposition</a></li> <li><a href="/wiki/Invertible_matrix" title="Invertible matrix">Invertible</a></li> <li><a href="/wiki/Minor_(linear_algebra)" title="Minor (linear algebra)">Minor</a></li> <li><a href="/wiki/Matrix_multiplication" title="Matrix multiplication">Multiplication</a></li> <li><a href="/wiki/Rank_(linear_algebra)" title="Rank (linear algebra)">Rank</a></li> <li><a href="/wiki/Transformation_matrix" title="Transformation matrix">Transformation</a></li> <li><a href="/wiki/Cramer%27s_rule" title="Cramer's rule">Cramer's rule</a></li> <li><a href="/wiki/Gaussian_elimination" title="Gaussian elimination">Gaussian elimination</a></li> <li><a href="/wiki/Productive_matrix" title="Productive matrix">Productive matrix</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bilinear_map" title="Bilinear map">Bilinear</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Orthogonality" title="Orthogonality">Orthogonality</a></li> <li><a href="/wiki/Dot_product" title="Dot product">Dot product</a></li> <li><a href="/wiki/Hadamard_product_(matrices)" title="Hadamard product (matrices)">Hadamard product</a></li> <li><a href="/wiki/Inner_product_space" title="Inner product space">Inner product space</a></li> <li><a href="/wiki/Outer_product" title="Outer product">Outer product</a></li> <li><a href="/wiki/Kronecker_product" title="Kronecker product">Kronecker product</a></li> <li><a href="/wiki/Gram%E2%80%93Schmidt_process" title="Gram–Schmidt process">Gram–Schmidt process</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Multilinear_algebra" title="Multilinear algebra">Multilinear algebra</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Determinant" title="Determinant">Determinant</a></li> <li><a href="/wiki/Cross_product" title="Cross product">Cross product</a></li> <li><a href="/wiki/Triple_product" title="Triple product">Triple product</a></li> <li><a href="/wiki/Seven-dimensional_cross_product" title="Seven-dimensional cross product">Seven-dimensional cross product</a></li> <li><a href="/wiki/Geometric_algebra" title="Geometric algebra">Geometric algebra</a></li> <li><a href="/wiki/Exterior_algebra" title="Exterior algebra">Exterior algebra</a></li> <li><a href="/wiki/Bivector" title="Bivector">Bivector</a></li> <li><a href="/wiki/Multivector" title="Multivector">Multivector</a></li> <li><a href="/wiki/Tensor" title="Tensor">Tensor</a></li> <li><a href="/wiki/Outermorphism" title="Outermorphism">Outermorphism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Vector_space" title="Vector space">Vector space</a> constructions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dual_space" title="Dual space">Dual</a></li> <li><a href="/wiki/Direct_sum_of_modules#Construction_for_two_vector_spaces" title="Direct sum of modules">Direct sum</a></li> <li><a href="/wiki/Function_space#In_linear_algebra" title="Function space">Function space</a></li> <li><a href="/wiki/Quotient_space_(linear_algebra)" title="Quotient space (linear algebra)">Quotient</a></li> <li><a href="/wiki/Linear_subspace" title="Linear subspace">Subspace</a></li> <li><a href="/wiki/Tensor_product" title="Tensor product">Tensor product</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Numerical_linear_algebra" title="Numerical linear algebra">Numerical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">Floating-point</a></li> <li><a href="/wiki/Numerical_stability" title="Numerical stability">Numerical stability</a></li> <li><a href="/wiki/Basic_Linear_Algebra_Subprograms" title="Basic Linear Algebra Subprograms">Basic Linear Algebra Subprograms</a></li> <li><a href="/wiki/Sparse_matrix" title="Sparse matrix">Sparse matrix</a></li> <li><a href="/wiki/Comparison_of_linear_algebra_libraries" title="Comparison of linear algebra libraries">Comparison of linear algebra libraries</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, 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