<?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>Matrix || Matrix -- join matrices vertically</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_matrix_lp__List_rp.html">next</a> | <a href="___Matrix_sp_vb_sp__Matrix.html">previous</a> | <a href="_matrix_lp__List_rp.html">forward</a> | <a href="___Matrix_sp_vb_sp__Matrix.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>Matrix || Matrix -- join matrices vertically</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>f = g || h</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="__vb_vb.html" title="a binary operator, often used for vertical concatenation">||</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>g</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a <tt>m</tt> by <tt>n</tt> matrix.</span></li> <li><span><tt>h</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a <tt>r</tt> by <tt>n</tt> matrix.</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, the <tt>m+r</tt> by <tt>n</tt> matrix, obtained from matrices <tt>g</tt> and <tt>h</tt> by concatenating the columns.</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = ZZ[i..p];</pre> </td></tr> <tr><td><pre>i2 : g = matrix {{i,j},{k,l}} o2 = | i j | | k l | 2 2 o2 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i3 : h = matrix {{m,n},{o,p}} o3 = | m n | | o p | 2 2 o3 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i4 : f= g || h o4 = | i j | | k l | | m n | | o p | 4 2 o4 : Matrix R <--- R</pre> </td></tr> </table> If one of the arguments is a ring element or an integer, then it will be multiplied by a suitable identity matrix.<table class="examples"><tr><td><pre>i5 : f || 33 o5 = {0} | i j | {0} | k l | {0} | m n | {0} | o p | {1} | 33 0 | {1} | 0 33 | 6 2 o5 : Matrix R <--- R</pre> </td></tr> </table> </div> </div> <div class="single"><h2>Caveat</h2> <div>It is assumed that the matrices <tt>g</tt> and <tt>h</tt> have the same <a href="___Ring.html" title="the class of all rings">Ring</a>.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></li> <li><span><a href="_ring.html" title="get the associated ring of an object">ring(Matrix)</a> -- get the associated ring of an object</span></li> </ul> </div> </div> </body> </html>