<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html> <!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ --> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <title>Permutation Matrix Functions (GNU Octave (version 5.1.0))</title> <meta name="description" content="Permutation Matrix Functions (GNU Octave (version 5.1.0))"> <meta name="keywords" content="Permutation Matrix Functions (GNU Octave (version 5.1.0))"> <meta name="resource-type" content="document"> <meta name="distribution" content="global"> <meta name="Generator" content="makeinfo"> <link href="index.html#Top" rel="start" title="Top"> <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index"> <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> <link href="Function-Support.html#Function-Support" rel="up" title="Function Support"> <link href="Example-Code.html#Example-Code" rel="next" title="Example Code"> <link href="Diagonal-Matrix-Functions.html#Diagonal-Matrix-Functions" rel="prev" title="Diagonal Matrix Functions"> <style type="text/css"> <!-- a.summary-letter {text-decoration: none} blockquote.indentedblock {margin-right: 0em} blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} blockquote.smallquotation {font-size: smaller} div.display {margin-left: 3.2em} div.example {margin-left: 3.2em} div.lisp {margin-left: 3.2em} div.smalldisplay {margin-left: 3.2em} div.smallexample {margin-left: 3.2em} div.smalllisp {margin-left: 3.2em} kbd {font-style: oblique} pre.display {font-family: inherit} pre.format {font-family: inherit} pre.menu-comment {font-family: serif} pre.menu-preformatted {font-family: serif} pre.smalldisplay {font-family: inherit; font-size: smaller} pre.smallexample {font-size: smaller} pre.smallformat {font-family: inherit; font-size: smaller} pre.smalllisp {font-size: smaller} span.nolinebreak {white-space: nowrap} span.roman {font-family: initial; font-weight: normal} span.sansserif {font-family: sans-serif; font-weight: normal} ul.no-bullet {list-style: none} --> </style> <link rel="stylesheet" type="text/css" href="octave.css"> </head> <body lang="en"> <a name="Permutation-Matrix-Functions"></a> <div class="header"> <p> Previous: <a href="Diagonal-Matrix-Functions.html#Diagonal-Matrix-Functions" accesskey="p" rel="prev">Diagonal Matrix Functions</a>, Up: <a href="Function-Support.html#Function-Support" accesskey="u" rel="up">Function Support</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p> </div> <hr> <a name="Permutation-Matrix-Functions-1"></a> <h4 class="subsection">21.3.2 Permutation Matrix Functions</h4> <a name="index-matrix_002c-permutation-functions"></a> <a name="index-permutation-matrix-functions"></a> <p><em>inv</em> and <em>pinv</em> will invert a permutation matrix, preserving its specialness. <em>det</em> can be applied to a permutation matrix, efficiently calculating the sign of the permutation (which is equal to the determinant). </p> <p>A permutation matrix can also be returned from the built-in functions <em>lu</em> and <em>qr</em>, if a pivoted factorization is requested. </p> <p>The <em>sparse</em> function will convert a permutation matrix efficiently to a sparse matrix. The <em>find</em> function will also work efficiently with a permutation matrix, making it possible to conveniently obtain the permutation indices. </p> </body> </html>