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About: M-matrix
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The set of non-singular M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices (i.e. matrices with inverses belonging to the class of positive matrices). The name M-matrix was seemingly originally chosen by Alexander Ostrowski in reference to Hermann Minkowski, who proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive." /> <meta property="og:site_name" content="DBpedia" /> <!-- /OpenGraph--> </head> <body about="http://dbpedia.org/resource/M-matrix"> <!-- navbar --> <nav class="navbar navbar-expand-md navbar-light bg-light fixed-top align-items-center"> <div class="container-xl"> <a class="navbar-brand" href="http://wiki.dbpedia.org/about" title="About DBpedia" style="color: #2c5078"> <img class="img-fluid" src="/statics/images/dbpedia_logo_land_120.png" alt="About DBpedia" /> </a> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#dbp-navbar" aria-controls="dbp-navbar" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="collapse navbar-collapse" id="dbp-navbar"> <ul 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endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div> <!-- /navbar --> <!-- page-header --> <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/M-matrix">M-matrix</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/ontology/AnatomicalStructure">anatomical structure</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In mathematics, especially linear algebra, an M-matrix is a Z-matrix with eigenvalues whose real parts are nonnegative. The set of non-singular M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices (i.e. matrices with inverses belonging to the class of positive matrices). The name M-matrix was seemingly originally chosen by Alexander Ostrowski in reference to Hermann Minkowski, who proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive.</p> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:abstract" lang="en" >In mathematics, especially linear algebra, an M-matrix is a Z-matrix with eigenvalues whose real parts are nonnegative. The set of non-singular M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices (i.e. matrices with inverses belonging to the class of positive matrices). The name M-matrix was seemingly originally chosen by Alexander Ostrowski in reference to Hermann Minkowski, who proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ja" >数学、特に線形代数の分野におけるM-行列（M-ぎょうれつ）とは、全ての固有値の実部が正であるようなZ-行列のことである。M-行列はP-行列の族の部分集合であり、また逆行列が正であるような行列の族の部分集合でもある。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >En mathématiques, une M-matrice est une matrice carrée réelle qui est à la fois une P-matrice et une Z-matrice, ce qui signifie que tous ses mineurs principaux sont strictement positifs et que ses éléments extra-diagonaux sont négatifs. D'autres caractérisations peuvent être utilisées, dont certaines sont données ci-dessous. Ces matrices interviennent dans l'étude des problèmes de complémentarité linéaire et dans certaines discrétisations d'opérateurs différentiels, en particulier ceux obéissant à un principe du maximum, comme le laplacien. Cette classe de matrices semble avoir été introduite par Alexander Ostrowski en référence à Hermann Minkowski.</span><small> (fr)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID"><small>dbo:</small>wikiPageID</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageID" datatype="xsd:integer" >7939066</span><small> (xsd:integer)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageLength"><small>dbo:</small>wikiPageLength</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageLength" datatype="xsd:nonNegativeInteger" >9362</span><small> (xsd:nonNegativeInteger)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageRevisionID"><small>dbo:</small>wikiPageRevisionID</a> </td><td 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property="rdfs:comment" lang="en" >In mathematics, especially linear algebra, an M-matrix is a Z-matrix with eigenvalues whose real parts are nonnegative. The set of non-singular M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices (i.e. matrices with inverses belonging to the class of positive matrices). The name M-matrix was seemingly originally chosen by Alexander Ostrowski in reference to Hermann Minkowski, who proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ja" >数学、特に線形代数の分野におけるM-行列（M-ぎょうれつ）とは、全ての固有値の実部が正であるようなZ-行列のことである。M-行列はP-行列の族の部分集合であり、また逆行列が正であるような行列の族の部分集合でもある。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >En mathématiques, une M-matrice est une matrice carrée réelle qui est à la fois une P-matrice et une Z-matrice, ce qui signifie que tous ses mineurs principaux sont strictement positifs et que ses éléments extra-diagonaux sont négatifs. D'autres caractérisations peuvent être utilisées, dont certaines sont données ci-dessous. Ces matrices interviennent dans l'étude des problèmes de complémentarité linéaire et dans certaines discrétisations d'opérateurs différentiels, en particulier ceux obéissant à un principe du maximum, comme le laplacien.</span><small> (fr)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >M-matrice</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ja" >M-行列</span><small> (ja)</small></span></li> <li><span class="literal"><span property="rdfs:label" lang="en" >M-matrix</span><small> (en)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 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