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<!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"><head><title>R: Calculate the Determinant of a Matrix</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for det {base}"><tr><td>det {base}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Calculate the Determinant of a Matrix</h2> <h3>Description</h3> <p><code>det</code> calculates the determinant of a matrix. <code>determinant</code> is a generic function that returns separately the modulus of the determinant, optionally on the logarithm scale, and the sign of the determinant. </p> <h3>Usage</h3> <pre> det(x, ...) determinant(x, logarithm = TRUE, ...) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>numeric matrix: logical matrices are coerced to numeric.</p> </td></tr> <tr valign="top"><td><code>logarithm</code></td> <td> <p>logical; if <code>TRUE</code> (default) return the logarithm of the modulus of the determinant.</p> </td></tr> <tr valign="top"><td><code>...</code></td> <td> <p>Optional arguments. At present none are used. Previous versions of <code>det</code> allowed an optional <code>method</code> argument. This argument will be ignored but will not produce an error.</p> </td></tr> </table> <h3>Details</h3> <p>The <code>determinant</code> function uses an LU decomposition and the <code>det</code> function is simply a wrapper around a call to <code>determinant</code>. </p> <p>Often, computing the determinant is <em>not</em> what you should be doing to solve a given problem. </p> <h3>Value</h3> <p>For <code>det</code>, the determinant of <code>x</code>. For <code>determinant</code>, a list with components </p> <table summary="R valueblock"> <tr valign="top"><td><code>modulus</code></td> <td> <p>a numeric value. The modulus (absolute value) of the determinant if <code>logarithm</code> is <code>FALSE</code>; otherwise the logarithm of the modulus.</p> </td></tr> <tr valign="top"><td><code>sign</code></td> <td> <p>integer; either <i>+1</i> or <i>-1</i> according to whether the determinant is positive or negative.</p> </td></tr> </table> <h3>Examples</h3> <pre> (x <- matrix(1:4, ncol = 2)) unlist(determinant(x)) det(x) det(print(cbind(1, 1:3, c(2,0,1)))) </pre> <hr /><div style="text-align: center;">[Package <em>base</em> version 3.6.0 <a href="00Index.html">Index</a>]</div> </body></html>