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<div><h1>submatrix(Matrix,VisibleList,VisibleList) -- select part 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>submatrix(f, rows, cols)</tt><br/><tt>submatrix(f,,cols)</tt><br/><tt>submatrix(f,rows,)</tt></div>
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<li><span>Function: <a href="_submatrix.html" title="">submatrix</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a map between free modules</span></li>
<li><span><tt>rows</tt>, <span>a <a href="___Visible__List.html">visible list</a></span>, a list of integers denoting the choice of rows. If omitted, use all rows</span></li>
<li><span><tt>cols</tt>, <span>a <a href="___Visible__List.html">visible list</a></span>, a list of integers denoting the choice of columns. If omitted, use all columns</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the submatrix of <tt>f</tt> corresponding to the lists <tt>rows</tt> and <tt>cols</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>Yields an r by c matrix, where r is the length of the list of integers <tt>rows</tt>, and c is the length of the list of integers <tt>cols</tt>. The <tt>(i,j)</tt>-th entry of the result is <tt>f_(rows_i, cols_j)</tt>.<p/>
Each list of integers may contain ranges and repetitions, as in <tt>{3, 5..7, 3:0}</tt><p/>
If <tt>rows</tt> or <tt>cols</tt> is omitted, all the corresponding indices are used.<p/>
Both <tt>rows</tt> and/or <tt>cols</tt> may contain duplicate values, in which case the result will contain duplicate rows and/or columns.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a .. o];</pre>
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<tr><td><pre>i2 : f = genericMatrix(R, a, 3, 5)
o2 = | a d g j m |
| b e h k n |
| c f i l o |
3 5
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : submatrix(f, {1,2,0}, {0..2, 4})
o3 = | b e h n |
| c f i o |
| a d g m |
3 4
o3 : Matrix R <--- R</pre>
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<table class="examples"><tr><td><pre>i4 : submatrix(f, {1,2}, )
o4 = | b e h k n |
| c f i l o |
2 5
o4 : Matrix R <--- R</pre>
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<tt>submatrix(f,,cols)</tt> can be written as <tt>submatrix(f,cols)</tt>, or <tt>f_cols</tt>.<table class="examples"><tr><td><pre>i5 : submatrix(f,,{0,1})
o5 = | a d |
| b e |
| c f |
3 2
o5 : Matrix R <--- R</pre>
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<tr><td><pre>i6 : f_{0,1}
o6 = | a d |
| b e |
| c f |
3 2
o6 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_submatrix_sq.html" title="exclude rows and/or columns of a matrix">submatrix'</a> -- exclude rows and/or columns of a matrix</span></li>
<li><span><a href="___Matrix_sp_us_sp__List.html" title="select columns">Matrix _ List</a> -- select columns</span></li>
<li><span><a href="___Matrix_sp^_sp__List.html" title="select rows">Matrix ^ List</a> -- select rows</span></li>
<li><span><a href="_submatrix_lp__Matrix_cm__Visible__List_rp.html" title="select columns">submatrix(Matrix,VisibleList)</a> -- select columns</span></li>
<li><span><a href="___Matrix_sp_us_sp__Array.html" title="component of map corresponding to summand of source">Matrix _ Array</a> -- component of map corresponding to summand of source</span></li>
<li><span><a href="___Matrix_sp^_sp__Array.html" title="component of map corresponding to summand of target">Matrix ^ Array</a> -- component of map corresponding to summand of target</span></li>
<li><span><a href="_null.html" title="the unique member of the empty class">null</a> -- the unique member of the empty class</span></li>
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