<html lang="en"> <head> <title>Permutation Matrix Functions - Untitled</title> <meta http-equiv="Content-Type" content="text/html"> <meta name="description" content="Untitled"> <meta name="generator" content="makeinfo 4.13"> <link title="Top" rel="start" href="index.html#Top"> <link rel="up" href="Function-Support.html#Function-Support" title="Function Support"> <link rel="prev" href="Diagonal-Matrix-Functions.html#Diagonal-Matrix-Functions" title="Diagonal Matrix Functions"> <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> <meta http-equiv="Content-Style-Type" content="text/css"> <style type="text/css"><!-- pre.display { font-family:inherit } pre.format { font-family:inherit } pre.smalldisplay { font-family:inherit; font-size:smaller } pre.smallformat { font-family:inherit; font-size:smaller } pre.smallexample { font-size:smaller } pre.smalllisp { font-size:smaller } span.sc { font-variant:small-caps } span.roman { font-family:serif; font-weight:normal; } span.sansserif { font-family:sans-serif; font-weight:normal; } --></style> </head> <body> <div class="node"> <a name="Permutation-Matrix-Functions"></a> <p> Previous: <a rel="previous" accesskey="p" href="Diagonal-Matrix-Functions.html#Diagonal-Matrix-Functions">Diagonal Matrix Functions</a>, Up: <a rel="up" accesskey="u" href="Function-Support.html#Function-Support">Function Support</a> <hr> </div> <h4 class="subsection">20.3.2 Permutation Matrix Functions</h4> <p><dfn>inv</dfn> and <dfn>pinv</dfn> will invert a permutation matrix, preserving its specialness. <dfn>det</dfn> can be applied to a permutation matrix, efficiently calculating the sign of the permutation (which is equal to the determinant). <p>A permutation matrix can also be returned from the built-in functions <dfn>lu</dfn> and <dfn>qr</dfn>, if a pivoted factorization is requested. <p>The <dfn>sparse</dfn> function will convert a permutation matrix efficiently to a sparse matrix. The <dfn>find</dfn> function will also work efficiently with a permutation matrix, making it possible to conveniently obtain the permutation indices. </body></html>