MSC2020 database

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> <title> MSC2020 database </title> <link rel="shortcut icon" href="https://www.ams.org/images/content/bubbles.png" type="image/x-icon"> <link rel="icon" href="https://www.ams.org/images/content/bubbles.png" type="image/x-icon"> <link rel="stylesheet" type="text/css" href="/mathscinet/css/print.css" /> <link rel="stylesheet" type="text/css" href="/mathscinet/javascript/jquery/jquery.autocomplete.css" /> <style type="text/css" media="screen"> @import url(/mathscinet/css/msn.css); </style> <link rel="stylesheet" type="text/css" href="/mathscinet/css/styles-primary.css" /> <style type="text/css"> body, input, select { font-family: Verdana, "Bitstream Vera Sans", Arial, Helvetica, sans-serif; } h3, ul.tabContainer, .erdosNumber, .helptopic, .helpsubtopic { font-family: "Trebuchet MS", "Bitstream 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class="tabContainer"> <li class="lowerTabEdge" id="tab1"> <div> <div> <a href="msc2010.html" onclick="return toggleTab( 'freeTools', 'tab1', 'folder1' )" id="tab1link" title=" MSC2010 database " accesskey="">MSC2010 database</a> </div> </div> </li> <li class="upperTab" id="tab2"> <div> <div> <a href="msc2020.html" onclick="return toggleTab( 'freeTools', 'tab2', 'folder2' )" id="tab2link" title=" MSC2020 database " accesskey="">MSC2020 database</a> </div> </div> </li> <li class="lowerTab" id="tab3"> <div> <div> <a href="useMSC.html" onclick="return toggleTab( 'freeTools', 'tab3', 'folder3' )" id="tab3link" title=" How to use the MSC " accesskey="">How to use the MSC</a> </div> </div> </li> </ul> <div class="topFolder" id="folder2"> <script type="text/javascript"> $(document).ready(function() { $("#search2").autocomplete("search.html",{autoFill:false, matchContains: 1, onItemSelect: function() {$("form").submit()}}); }); </script> <div class="folderWrap1"> <div class="folderWrap2"> <div class="folderWrap4"> <div class="folderContent"> <form name="searchMSC2" method="get" action="msc2020.html" style="width: auto;"> <div class="summary" id="summary2"> </div> <br style="clear: both;" /> <div class="widgets"> <div class="controlsPosition2"> <h3>Browse Classification</h3> <span class="enter_msc" style="float:both;">Select a 2 digit classification</span><br /> <select name="t" id="selectTarget2" tabindex="1" onchange="if (this.value != '') { this.form.elements[2].click(); }"> <option value="">Select a Mathematics subject classification</option> <option value="00-XX">00 General and overarching topics; collections</option> <option value="01-XX">01 History and biography</option> <option value="03-XX">03 Mathematical logic and foundations</option> <option value="05-XX">05 Combinatorics </option> <option value="06-XX">06 Order, lattices, ordered algebraic structures</option> <option value="08-XX">08 General algebraic systems</option> <option value="11-XX">11 Number theory</option> <option value="12-XX">12 Field theory and polynomials</option> <option value="13-XX">13 Commutative algebra</option> <option value="14-XX">14 Algebraic geometry</option> <option selected="selected" value="15A69">15 Linear and multilinear algebra; matrix theory</option> <option value="16-XX">16 Associative rings and algebras </option> <option value="17-XX">17 Nonassociative rings and algebras</option> <option value="18-XX">18 Category theory; homological algebra </option> <option value="19-XX">19 $K$-theory</option> <option value="20-XX">20 Group theory and generalizations</option> <option value="22-XX">22 Topological groups, Lie groups </option> <option value="26-XX">26 Real functions</option> <option value="28-XX">28 Measure and integration </option> <option value="30-XX">30 Functions of a complex variable</option> <option value="31-XX">31 Potential theory </option> <option value="32-XX">32 Several complex variables and analytic spaces </option> <option value="33-XX">33 Special functions (33-XX deals with the properties of functions as functions) </option> <option value="34-XX">34 Ordinary differential equations</option> <option value="35-XX">35 Partial differential equations</option> <option value="37-XX">37 Dynamical systems and ergodic theory</option> <option value="39-XX">39 Difference and functional equations</option> <option value="40-XX">40 Sequences, series, summability</option> <option value="41-XX">41 Approximations and expansions </option> <option value="42-XX">42 Harmonic analysis on Euclidean spaces</option> <option value="43-XX">43 Abstract harmonic analysis </option> <option value="44-XX">44 Integral transforms, operational calculus </option> <option value="45-XX">45 Integral equations</option> <option value="46-XX">46 Functional analysis </option> <option value="47-XX">47 Operator theory</option> <option value="49-XX">49 Calculus of variations and optimal control; optimization</option> <option value="51-XX">51 Geometry </option> <option value="52-XX">52 Convex and discrete geometry</option> <option value="53-XX">53 Differential geometry </option> <option value="54-XX">54 General topology </option> <option value="55-XX">55 Algebraic topology</option> <option value="57-XX">57 Manifolds and cell complexes </option> <option value="58-XX">58 Global analysis, analysis on manifolds</option> <option value="60-XX">60 Probability theory and stochastic processes </option> <option value="62-XX">62 Statistics</option> <option value="65-XX">65 Numerical analysis</option> <option value="68-XX">68 Computer science </option> <option value="70-XX">70 Mechanics of particles and systems </option> <option value="74-XX">74 Mechanics of deformable solids</option> <option value="76-XX">76 Fluid mechanics </option> <option value="78-XX">78 Optics, electromagnetic theory </option> <option value="80-XX">80 Classical thermodynamics, heat transfer </option> <option value="81-XX">81 Quantum theory</option> <option value="82-XX">82 Statistical mechanics, structure of matter</option> <option value="83-XX">83 Relativity and gravitational theory</option> <option value="85-XX">85 Astronomy and astrophysics </option> <option value="86-XX">86 Geophysics</option> <option value="90-XX">90 Operations research, mathematical programming</option> <option value="91-XX">91 Game theory, economics, finance, and other social and behavioral sciences</option> <option value="92-XX">92 Biology and other natural sciences</option> <option value="93-XX">93 Systems theory; control </option> <option value="94-XX">94 Information and communication theory, circuits</option> <option value="97-XX">97 Mathematics education</option> </select> </div> <div class="controlsPosition"> <h3>Search Classifications</h3> <span class="enter_msc">Enter a keyword, phrase or a 2-, 3-, or 5-digit classification</span><br /> <input size="40" autocomplete="off" name="s" value="" id="search2" /> <div class="buttonBox"> <input name="btn" type="submit" value="Search" class="button" /> </div> </div> </div> <input type="hidden" name="ls" value="Ct" /> <div class="resultSet" id="resultSet2"> <div class="buttonBox"> <input type="submit" name="btn" value="Clear" class="button" /> </div> <span class="legend"> < <a href="msc2020.html?t=&btn=Current"></a> | <a href="msc2020.html?t=15-XX&btn=Current">15-XX</a> | <a href="msc2020.html?t=15Bxx&btn=Current">15Bxx</a> > </span> <table class="results"> <tr class="current"> <td><a href="msc2020.html?t=15-XX&btn=Current" title=""><b>15-XX</b></a></td> <td></td> <td></td> <td><b>Linear and multilinear algebra; matrix theory</b></td> </tr> <tr class="current"> <td></td> <td><a href="msc2020.html?t=15Axx&btn=Current" title="">15Axx</a></td> <td></td> <td>Basic linear algebra</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A03  </td> <td>Vector spaces, linear dependence, rank, lineability</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A04  </td> <td>Linear transformations, semilinear transformations</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A06  </td> <td>Linear equations (linear algebraic aspects)</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A09  </td> <td>Theory of matrix inversion and generalized inverses</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A10  </td> <td>Applications of generalized inverses</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A12  </td> <td>Conditioning of matrices [See also <a href="msc2020.html?t=65F35&btn=Current">65F35</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A15  </td> <td>Determinants, permanents, traces, other special matrix functions [See also <a href="msc2020.html?t=19B10&btn=Current">19B10</a>, <a href="msc2020.html?t=19B14&btn=Current">19B14</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A16  </td> <td>Matrix exponential and similar functions of matrices</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A18  </td> <td>Eigenvalues, singular values, and eigenvectors</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A20  </td> <td>Diagonalization, Jordan forms</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A21  </td> <td>Canonical forms, reductions, classification</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A22  </td> <td>Matrix pencils [See also <a href="msc2020.html?t=47A56&btn=Current">47A56</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A23  </td> <td>Factorization of matrices</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A24  </td> <td>Matrix equations and identities</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A27  </td> <td>Commutativity of matrices</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A29  </td> <td>Inverse problems in linear algebra</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A30  </td> <td>Algebraic systems of matrices [See also <a href="msc2020.html?t=16S50&btn=Current">16S50</a>, <a href="msc2020.html?t=20Gxx&btn=Current">20Gxx</a>, <a href="msc2020.html?t=20Hxx&btn=Current">20Hxx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A39  </td> <td>Linear inequalities of matrices</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A42  </td> <td>Inequalities involving eigenvalues and eigenvectors</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A45  </td> <td>Miscellaneous inequalities involving matrices</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A54  </td> <td>Matrices over function rings in one or more variables</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A60  </td> <td>Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also <a href="msc2020.html?t=65F35&btn=Current">65F35</a>, <a href="msc2020.html?t=65J05&btn=Current">65J05</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A63  </td> <td>Quadratic and bilinear forms, inner products [See mainly <a href="msc2020.html?t=11Exx&btn=Current">11Exx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A66  </td> <td>Clifford algebras, spinors</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A67  </td> <td>Applications of Clifford algebras to physics, etc.</td> </tr> <tr class="current"> <td></td> <td></td> <td><span class="highlight">15A69</span>  </td> <td>Multilinear algebra, tensor calculus</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A72  </td> <td>Vector and tensor algebra, theory of invariants [See also <a href="msc2020.html?t=13A50&btn=Current">13A50</a>, <a href="msc2020.html?t=14L24&btn=Current">14L24</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A75  </td> <td>Exterior algebra, Grassmann algebras</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A78  </td> <td>Other algebras built from modules</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A80  </td> <td>Max-plus and related algebras</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A83  </td> <td>Matrix completion problems</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A86  </td> <td>Linear preserver problems</td> </tr> <tr class="current"> <td></td> <td></td> <td>15A99  </td> <td>None of the above, but in this section</td> </tr> </table> <div class="buttonBox"> <input type="submit" name="btn" value="Clear" class="button" /> </div> <span class="legend"> < <a href="msc2020.html?t=&btn=Current"></a> | <a href="msc2020.html?t=15-XX&btn=Current">15-XX</a> | <a href="msc2020.html?t=15Bxx&btn=Current">15Bxx</a> > </span> </div> </form> </div> <div class="folderFooter"><div class="left"> </div><div class="right"> </div></div> </div> </div> </div> <div class="copyright"> <a href="http://www.ams.org/ams/copyright.html">© Copyright 2024, American Mathematical Society</a><br /> <a href="http://www.ams.org/ams/privacy.html">Privacy Statement</a> </div> <div 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MSC2020 database