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It is often used in iteration theory to find the continuous iteration of functions which cannot be iterated by pattern recognition alone. Other uses of Carleman matrices occur in the theory of probability generating functions, and Markov chains." /> <meta property="og:site_name" content="DBpedia" />  </head> <body about="http://dbpedia.org/resource/Carleman_matrix">  <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"> </button> <div class="collapse navbar-collapse" id="dbp-navbar"> <ul class="navbar-nav me-auto mb-2 mb-lg-0"> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownBrowse" role="button" data-bs-toggle="dropdown" 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href="http://dbpedia.org/resource/Carleman_matrix">Carleman matrix</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://dbpedia.org/ontology/AnatomicalStructure">anatomical structure</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In mathematics, a Carleman matrix is a matrix used to convert function composition into matrix multiplication. It is often used in iteration theory to find the continuous iteration of functions which cannot be iterated by pattern recognition alone. Other uses of Carleman matrices occur in the theory of probability generating functions, and Markov chains. </div> </div> </div> </section>   <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">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li>In mathematics, a Carleman matrix is a matrix used to convert function composition into matrix multiplication. It is often used in iteration theory to find the continuous iteration of functions which cannot be iterated by pattern recognition alone. Other uses of Carleman matrices occur in the theory of probability generating functions, and Markov chains. (en)</li> <li style="display:none;">数学におけるカーレマン行列（カーレマンぎょうれつ、英: Carleman matrix）は、函数の合成を行列の積に読み替えるために用いられる行列である。反復理論において、パターン認識のみでは反復の出来ない連続な反復函数を見つけるために用いられる。その他、確率母函数やマルコフ連鎖の理論で用いられる。 (ja)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink">dbo:wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://www.jstor.org/stable/2032522" href="https://www.jstor.org/stable/2032522">https://www.jstor.org/stable/2032522</a></li> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://arxiv.org/abs/math-ph/0002044" href="https://arxiv.org/abs/math-ph/0002044">https://arxiv.org/abs/math-ph/0002044</a></li> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://arxiv.org/abs/math/9207221" href="https://arxiv.org/abs/math/9207221">https://arxiv.org/abs/math/9207221</a></li> <li><a class="uri" 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resource="http://dbpedia.org/class/yago/WikicatFunctionsAndMappings" href="http://dbpedia.org/class/yago/WikicatFunctionsAndMappings">yago:WikicatFunctionsAndMappings</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li>In mathematics, a Carleman matrix is a matrix used to convert function composition into matrix multiplication. It is often used in iteration theory to find the continuous iteration of functions which cannot be iterated by pattern recognition alone. Other uses of Carleman matrices occur in the theory of probability generating functions, and Markov chains. (en)</li> <li style="display:none;">数学におけるカーレマン行列（カーレマンぎょうれつ、英: Carleman matrix）は、函数の合成を行列の積に読み替えるために用いられる行列である。反復理論において、パターン認識のみでは反復の出来ない連続な反復函数を見つけるために用いられる。その他、確率母函数やマルコフ連鎖の理論で用いられる。 (ja)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li>Carleman matrix (en)</li> <li style="display:none;">カーレマン行列 (ja)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs">owl:sameAs</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.03d0fd3" href="http://rdf.freebase.com/ns/m.03d0fd3">freebase:Carleman matrix</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://yago-knowledge.org/resource/Carleman_matrix" href="http://yago-knowledge.org/resource/Carleman_matrix">yago-res:Carleman matrix</a></li> <li><a class="uri" rel="owl:sameAs" 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