<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- --> <!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html --> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head><title>determinant -- determinant of a matrix</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_determinant_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">next</a> | <a href="___Description.html">previous</a> | <a href="_determinant_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">forward</a> | <a href="___Description.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div> </td> </tr> </table> <hr/> <div><h1>determinant -- determinant of a matrix</h1> <div class="single"><h2>Synopsis</h2> <ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>det M</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>M</tt>, a square <a href="___Matrix.html">matrix</a></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Element.html">ring element</a></span>, which is the determinant of <tt>M</tt></span></li> </ul> </div> </li> <li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_determinant_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, -- choose between Bareiss and Cofactor algorithms</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = QQ[vars(0..8)] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : M = genericMatrix(R,2,2) o2 = | a c | | b d | 2 2 o2 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i3 : det M o3 = - b*c + a*d o3 : R</pre> </td></tr> <tr><td><pre>i4 : N = genericMatrix(R,3,3) o4 = | a d g | | b e h | | c f i | 3 3 o4 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i5 : det N o5 = - c*e*g + b*f*g + c*d*h - a*f*h - b*d*i + a*e*i o5 : R</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_exterior__Power.html" title="exterior power">exteriorPower</a> -- exterior power</span></li> <li><span><a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors</a> -- ideal generated by minors</span></li> <li><span><a href="_permanents.html" title="ideal generated by square permanents of a matrix">permanents</a> -- ideal generated by square permanents of a matrix</span></li> <li><span><a href="_pfaffians.html" title="ideal generated by Pfaffians">pfaffians</a> -- ideal generated by Pfaffians</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>determinant</tt> :</h2> <ul><li>determinant(Matrix)</li> </ul> </div> </div> </body> </html>