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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>7 Matrices and Linear Algebra</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="../racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-style.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../doc-site.css" title="default"/><script type="text/javascript" src="../scribble-common.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../doc-site.js"></script><script type="text/javascript" src="../local-redirect/local-redirect.js"></script><script type="text/javascript" src="../local-redirect/local-user-redirect.js"></script><!--[if IE 6]><style type="text/css">.SIEHidden { overflow: hidden; }</style><![endif]--></head><body id="doc-racket-lang-org"><div class="tocset"><div class="tocview"><div class="tocviewlist tocviewlisttopspace"><div class="tocviewtitle"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_0");">►</a></td><td></td><td><a href="index.html" class="tocviewlink" data-pltdoc="x">Math Library</a></td></tr></table></div><div class="tocviewsublisttop" style="display: none;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="base.html" class="tocviewlink" data-pltdoc="x">Constants and Elementary Functions</a></td></tr><tr><td align="right">2 </td><td><a href="flonum.html" class="tocviewlink" data-pltdoc="x">Flonums</a></td></tr><tr><td align="right">3 </td><td><a href="special.html" class="tocviewlink" data-pltdoc="x">Special Functions</a></td></tr><tr><td align="right">4 </td><td><a href="number-theory.html" class="tocviewlink" data-pltdoc="x">Number Theory</a></td></tr><tr><td align="right">5 </td><td><a href="bigfloat.html" class="tocviewlink" data-pltdoc="x">Arbitrary-<wbr></wbr>Precision Floating-<wbr></wbr>Point Numbers (<a name="(tech._bigfloat)"></a><span style="font-style: italic">Bigfloats</span>)</a></td></tr><tr><td align="right">6 </td><td><a href="array.html" class="tocviewlink" data-pltdoc="x">Arrays</a></td></tr><tr><td align="right">7 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Matrices and Linear Algebra</a></td></tr><tr><td align="right">8 </td><td><a href="stats.html" class="tocviewlink" data-pltdoc="x">Statistics Functions</a></td></tr><tr><td align="right">9 </td><td><a href="dist.html" class="tocviewlink" data-pltdoc="x">Probability Distributions</a></td></tr><tr><td align="right">10 </td><td><a href="utils.html" class="tocviewlink" data-pltdoc="x">Stuff That Doesn’t Belong Anywhere Else</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_1");">▼</a></td><td>7 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Matrices and Linear Algebra</a></td></tr></table><div class="tocviewsublistbottom" style="display: block;" id="tocview_1"><table cellspacing="0" cellpadding="0"><tr><td align="right">7.1 </td><td><a href="matrix_intro.html" class="tocviewlink" data-pltdoc="x">Introduction</a></td></tr><tr><td align="right">7.2 </td><td><a href="matrix_types.html" class="tocviewlink" data-pltdoc="x">Types, Predicates and Accessors</a></td></tr><tr><td align="right">7.3 </td><td><a href="matrix_construction.html" class="tocviewlink" data-pltdoc="x">Construction</a></td></tr><tr><td align="right">7.4 </td><td><a href="matrix_conversion.html" class="tocviewlink" data-pltdoc="x">Conversion</a></td></tr><tr><td align="right">7.5 </td><td><a href="matrix_arith.html" class="tocviewlink" data-pltdoc="x">Entrywise Operations and Arithmetic</a></td></tr><tr><td align="right">7.6 </td><td><a href="matrix_poly.html" class="tocviewlink" data-pltdoc="x">Polymorphic Operations</a></td></tr><tr><td align="right">7.7 </td><td><a href="matrix_basic.html" class="tocviewlink" data-pltdoc="x">Basic Operations</a></td></tr><tr><td align="right">7.8 </td><td><a href="matrix_inner.html" class="tocviewlink" data-pltdoc="x">Inner Product Space Operations</a></td></tr><tr><td align="right">7.9 </td><td><a href="matrix_solve.html" class="tocviewlink" data-pltdoc="x">Solving Systems of Equations</a></td></tr><tr><td align="right">7.10 </td><td><a href="matrix_row-alg.html" class="tocviewlink" data-pltdoc="x">Row-<wbr></wbr>Based Algorithms</a></td></tr><tr><td align="right">7.11 </td><td><a href="matrix_ortho-alg.html" class="tocviewlink" data-pltdoc="x">Orthogonal Algorithms</a></td></tr><tr><td align="right">7.12 </td><td><a href="matrix_op-norm.html" class="tocviewlink" data-pltdoc="x">Operator Norms and Comparing Matrices</a></td></tr></table></div></div></div></div><div class="maincolumn"><div class="main"><div class="versionbox"><span class="version">6.7</span></div><div class="navsettop"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "6.7", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.7");">top</a></span><span class="navright"> <a href="array_strict.html" title="backward to "6.16 Strictness"" data-pltdoc="x">← prev</a> <a href="index.html" title="up to "Math Library"" data-pltdoc="x">up</a> <a href="matrix_intro.html" title="forward to "7.1 Introduction"" data-pltdoc="x">next →</a></span> </div><h3 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""matrices"">7<tt> </tt><a name="(part._matrices)"></a><a name="(mod-path._math/matrix)"></a>Matrices and Linear Algebra</h3><div class="SAuthorListBox"><span class="SAuthorList"><p class="author">Jens Axel Søgaard <<a href="mailto:jensaxel@soegaard.net">jensaxel@soegaard.net</a>></p><span class="SAuthorSep"><br/></span><p class="author">Neil Toronto <<a href="mailto:ntoronto@racket-lang.org">ntoronto@racket-lang.org</a>></p></span></div><p><div class="SIntrapara"></div><div class="SIntrapara"></div></p><p><span style="font-weight: bold">Performance Warning:</span> Matrix values are arrays, as exported by <a href="array.html" class="RktModLink" data-pltdoc="x"><span class="RktSym">math/array</span></a>.
The same performance warning applies: operations are currently 25-50 times slower in untyped Racket
than in Typed Racket, due to the overhead of checking higher-order contracts. We are working on it.</p><p>For now, if you need speed, use the <a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=index.html&version=6.7" class="RktModLink Sq" data-pltdoc="x"><span class="RktSym">typed/racket</span></a> language.</p><p><table cellspacing="0" cellpadding="0" class="defmodule"><tr><td align="left"><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._require%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">require</a></span><span class="stt"> </span><a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">math/matrix</span></a><span class="RktPn">)</span></td><td align="right"><span class="RpackageSpec"><span class="Smaller"> package:</span> <span class="stt">math-lib</span></span></td></tr></table></p><p><div class="SIntrapara">Like all of <a href="index.html" class="RktModLink" data-pltdoc="x"><span class="RktSym">math</span></a>, <a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">math/matrix</span></a> is a work in progress.
Most of the basic algorithms are implemented, but some are still in planning.
Possibly the most useful unimplemented algorithms are
</div><div class="SIntrapara"><ul><li><p>LUP decomposition (currently, LU decomposition is implemented, in <span class="RktSym"><a href="matrix_row-alg.html#%28def._%28%28lib._math%2Fmatrix..rkt%29._matrix-lu%29%29" class="RktValLink" data-pltdoc="x">matrix-lu</a></span>)</p></li><li><p><span class="RktSym"><a href="matrix_solve.html#%28def._%28%28lib._math%2Fmatrix..rkt%29._matrix-solve%29%29" class="RktValLink" data-pltdoc="x">matrix-solve</a></span> for triangular matrices</p></li><li><p>Singular value decomposition (SVD)</p></li><li><p>Eigendecomposition</p></li><li><p>Decomposition-based solvers</p></li><li><p>Pseudoinverse and least-squares solving</p></li></ul></div></p><table cellspacing="0" cellpadding="0"><tr><td><p><span class="hspace"> </span><a href="matrix_intro.html" class="toclink" data-pltdoc="x">7.1<span class="hspace"> </span>Introduction</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_intro.html#%28part._matrix~3afunction-types%29" class="toclink" data-pltdoc="x">7.1.1<span class="hspace"> </span>Function Types</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_intro.html#%28part._matrix~3afailure%29" class="toclink" data-pltdoc="x">7.1.2<span class="hspace"> </span>Failure Arguments</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_intro.html#%28part._matrix~3abroadcasting%29" class="toclink" data-pltdoc="x">7.1.3<span class="hspace"> </span>Broadcasting</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_intro.html#%28part._.Strictness%29" class="toclink" data-pltdoc="x">7.1.4<span class="hspace"> </span>Strictness</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_types.html" class="toclink" data-pltdoc="x">7.2<span class="hspace"> </span>Types, Predicates and Accessors</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_construction.html" class="toclink" data-pltdoc="x">7.3<span class="hspace"> </span>Construction</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_conversion.html" class="toclink" data-pltdoc="x">7.4<span class="hspace"> </span>Conversion</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_arith.html" class="toclink" data-pltdoc="x">7.5<span class="hspace"> </span>Entrywise Operations and Arithmetic</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_poly.html" class="toclink" data-pltdoc="x">7.6<span class="hspace"> </span>Polymorphic Operations</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_basic.html" class="toclink" data-pltdoc="x">7.7<span class="hspace"> </span>Basic Operations</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_inner.html" class="toclink" data-pltdoc="x">7.8<span class="hspace"> </span>Inner Product Space Operations</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_solve.html" class="toclink" data-pltdoc="x">7.9<span class="hspace"> </span>Solving Systems of Equations</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_row-alg.html" class="toclink" data-pltdoc="x">7.10<span class="hspace"> </span>Row-Based Algorithms</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_ortho-alg.html" class="toclink" data-pltdoc="x">7.11<span class="hspace"> </span>Orthogonal Algorithms</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="matrix_op-norm.html" class="toclink" data-pltdoc="x">7.12<span class="hspace"> </span>Operator Norms and Comparing Matrices</a></p></td></tr></table><div class="navsetbottom"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "6.7", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.7");">top</a></span><span class="navright"> <a href="array_strict.html" title="backward to "6.16 Strictness"" data-pltdoc="x">← prev</a> <a href="index.html" title="up to "Math Library"" data-pltdoc="x">up</a> <a href="matrix_intro.html" title="forward to "7.1 Introduction"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
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