EVOLUTION-MANAGER
Edit File: Null.html
<!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: Null Spaces of Matrices</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 Null {MASS}"><tr><td>Null {MASS}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2> Null Spaces of Matrices </h2> <h3>Description</h3> <p>Given a matrix, <code>M</code>, find a matrix <code>N</code> giving a basis for the (left) null space. That is <code>crossprod(N, M) = t(N) %*% M</code> is an all-zero matrix and <code>N</code> has the maximum number of linearly independent columns. </p> <h3>Usage</h3> <pre> Null(M) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>M</code></td> <td> <p>Input matrix. A vector is coerced to a 1-column matrix. </p> </td></tr> </table> <h3>Details</h3> <p>For a basis for the (right) null space <i>{x : Mx = 0}</i>, use <code>Null(t(M))</code>. </p> <h3>Value</h3> <p>The matrix <code>N</code> with the basis for the (left) null space, or a matrix with zero columns if the matrix <code>M</code> is square and of maximal rank. </p> <h3>References</h3> <p>Venables, W. N. and Ripley, B. D. (2002) <em>Modern Applied Statistics with S.</em> Fourth edition. Springer. </p> <h3>See Also</h3> <p><code><a href="../../base/html/qr.html">qr</a></code>, <code><a href="../../base/html/qraux.html">qr.Q</a></code>. </p> <h3>Examples</h3> <pre> # The function is currently defined as function(M) { tmp <- qr(M) set <- if(tmp$rank == 0L) seq_len(ncol(M)) else -seq_len(tmp$rank) qr.Q(tmp, complete = TRUE)[, set, drop = FALSE] } </pre> <hr /><div style="text-align: center;">[Package <em>MASS</em> version 7.3-51.4 <a href="00Index.html">Index</a>]</div> </body></html>