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<head><title>Matrix ++ Matrix -- direct sum of maps</title>
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<div><h1>Matrix ++ Matrix -- direct sum of maps</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><span>Operator: <a href="__pl_pl.html" title="a binary operator, usually used for direct sum">++</a></span></li>
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<div class="single"><h2>Description</h2>
<div><tt>f++g</tt> -- computes the direct sum of two maps between modules.<p/>
If an argument is a ring element or integer, it is promoted to a one by one matrix.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..c];</pre>
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<tr><td><pre>i2 : vars R ++ transpose vars R
o2 = {0} | a b c 0 |
{-1} | 0 0 0 a |
{-1} | 0 0 0 b |
{-1} | 0 0 0 c |
4 4
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : oo^[1]
o3 = {-1} | 0 0 0 a |
{-1} | 0 0 0 b |
{-1} | 0 0 0 c |
3 4
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : a++b++c
o4 = | a 0 0 |
| 0 b 0 |
| 0 0 c |
3 3
o4 : Matrix R <--- R</pre>
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Selecting rows or columns of blocks:<ul><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="___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>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a> -- direct sum of modules or maps</span></li>
<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="___Matrix_sp_vb_vb_sp__Matrix.html" title="join matrices vertically">Matrix || Matrix</a> -- join matrices vertically</span></li>
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