<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >title >GAP (LinearAlgebraForCAP) - Chapter 1: Category of Matrices</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chap1" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chapInd.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap0.html" >[Previous Chapter]</a> <a href="chap2.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap1_mj.html" >[MathJax on]</a></p>"X79A2BF518637FFB7" name="X79A2BF518637FFB7" ></a></p>div class="ChapSects" ><a href="chap1.html#X79A2BF518637FFB7" >1 <span class="Heading" >Category of Matrices</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X86EC0F0A78ECBC10" >1.1 <span class="Heading" >Constructors</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X79D9727280354457" >1.1-1 MatrixCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7C6DB0457A656406" >1.1-2 VectorSpaceMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7EB162887B8F8708" >1.1-3 VectorSpaceObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X818AE01E7C9D21A5" >1.1-4 MatrixCategoryObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7A0CAF7F7CE754E7" >1.1-5 MatrixCategory_as_CategoryOfRows</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7C701DBF7BAE649A" >1.2 <span class="Heading" >Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7A25998E79499AE8" >1.2-1 UnderlyingFieldForHomalg</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8513433F7DA84E66" >1.2-2 UnderlyingMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X83D0E5BD8763C8FD" >1.2-3 UnderlyingFieldForHomalg</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X81C6A5F382A1D4F5" >1.2-4 Dimension</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7D03633A7D98026B" >1.3 <span class="Heading" >GAP Categories</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7DAEE1D67CDFA35A" >1.3-1 IsVectorSpaceMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7EF7321D794F9050" >1.3-2 IsVectorSpaceObject</a></span >div ></div >div >span class="Heading" >Category of Matrices</span ></h3>"X86EC0F0A78ECBC10" name="X86EC0F0A78ECBC10" ></a></p>span class="Heading" >Constructors</span ></h4>"X79D9727280354457" name="X79D9727280354457" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ MatrixCategory</code >( <var class="Arg" >F</var > )</td ><td class="tdright" >( operation )</td ></tr ></table ></div >span class="Math" >F</span >. The output is the matrix category over <span class="Math" >F</span >. Objects in this category are non-negative integers. Morphisms from a non-negative integer <span class="Math" >m</span > to a non-negative integer <span class="Math" >n</span > are given by <span class="Math" >m \times n</span > matrices.</p>"X7C6DB0457A656406" name="X7C6DB0457A656406" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ VectorSpaceMorphism</code >( <var class="Arg" >S</var >, <var class="Arg" >M</var >, <var class="Arg" >R</var > )</td ><td class="tdright" >( operation )</td ></tr ></table ></div >span class="Math" >\mathrm{Hom}(S,R)</span ></p>object <span class="Math" >S</span > in the category of matrices over a homalg field <span class="Math" >F</span >, a homalg matrix <span class="Math" >M</span > over <span class="Math" >F</span >, and another object <span class="Math" >R</span > in the category of matrices over <span class="Math" >F</span >. The output is the morphism <span class="Math" >S \rightarrow R</span > in the category of matrices over <span class="Math" >F</span > whose underlying matrix is given by <span class="Math" >M</span >.</p>"X7EB162887B8F8708" name="X7EB162887B8F8708" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ VectorSpaceObject</code >( <var class="Arg" >d</var >, <var class="Arg" >F</var > )</td ><td class="tdright" >( operation )</td ></tr ></table ></div >object </p>span class="Math" >d</span > and a homalg field <span class="Math" >F</span >. The output is an object in the category of matrices over <span class="Math" >F</span > of dimension <span class="Math" >d</span >. This function delegates to <code class="code" >MatrixCategoryObject</code >.</p>"X818AE01E7C9D21A5" name="X818AE01E7C9D21A5" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ MatrixCategoryObject</code >( <var class="Arg" >cat</var >, <var class="Arg" >d</var > )</td ><td class="tdright" >( operation )</td ></tr ></table ></div >object </p>span class="Math" >cat</span > over a field and a non-negative integer <span class="Math" >d</span >. The output is an object in <span class="Math" >cat</span > of dimension <span class="Math" >d</span >.</p>"X7A0CAF7F7CE754E7" name="X7A0CAF7F7CE754E7" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ MatrixCategory_as_CategoryOfRows</code >( <var class="Arg" >F</var > )</td ><td class="tdright" >( operation )</td ></tr ></table ></div >span class="Math" >F</span >. The output is the matrix category over <span class="Math" >F</span >, constructed internally as a wrapper category of the <code class="code" >CategoryOfRows</code > of <span class="Math" >F</span >. Only available if the package <code class="code" >AdditiveClosuresForCAP</code > is available.</p>"X7C701DBF7BAE649A" name="X7C701DBF7BAE649A" ></a></p>span class="Heading" >Attributes</span ></h4>"X7A25998E79499AE8" name="X7A25998E79499AE8" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ UnderlyingFieldForHomalg</code >( <var class="Arg" >alpha</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >span class="Math" >\alpha</span > in the matrix category over a homalg field <span class="Math" >F</span >. The output is the field <span class="Math" >F</span >.</p>"X8513433F7DA84E66" name="X8513433F7DA84E66" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ UnderlyingMatrix</code >( <var class="Arg" >alpha</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >span class="Math" >\alpha</span > in a matrix category. The output is its underlying matrix <span class="Math" >M</span >.</p>"X83D0E5BD8763C8FD" name="X83D0E5BD8763C8FD" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ UnderlyingFieldForHomalg</code >( <var class="Arg" >A</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >object <span class="Math" >A</span > in the matrix category over a homalg field <span class="Math" >F</span >. The output is the field <span class="Math" >F</span >.</p>"X81C6A5F382A1D4F5" name="X81C6A5F382A1D4F5" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ Dimension</code >( <var class="Arg" >A</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >object <span class="Math" >A</span > in a matrix category. The output is the dimension of <span class="Math" >A</span >.</p>"X7D03633A7D98026B" name="X7D03633A7D98026B" ></a></p>span class="Heading" >GAP Categories</span ></h4>"X7DAEE1D67CDFA35A" name="X7DAEE1D67CDFA35A" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsVectorSpaceMorphism</code >( <var class="Arg" >object </var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>span class="Math" >F</span >.</p>"X7EF7321D794F9050" name="X7EF7321D794F9050" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsVectorSpaceObject</code >( <var class="Arg" >object </var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>span class="Math" >F</span >.</p>div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap0.html" >[Previous Chapter]</a> <a href="chap2.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html >quality 100%
¤ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
¤ *© Formatika GbR, Deutschland
