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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_matrices.html" title="">matrices</a> > <a href="_concatenating_spmatrices.html" title="">concatenating matrices</a></div>
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<div><h1>concatenating matrices</h1>
<div>Before Macaulay2 can concatenate matrices, the matrices in question <em>must</em> have entries in the same ring.<h2>concatenate horizontally</h2>
Use <a href="__vb.html" title="a binary operator, often used for horizontal concatenation">|</a> to concatenate two matrices horizontally.<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[a..f];</pre>
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<tr><td><pre>i2 : M = genericMatrix(R,a,3,2)
o2 = | a d |
| b e |
| c f |
3 2
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : N = matrix{{d^2,a*d},{b*c,b*d},{a,c}}
o3 = | d2 ad |
| bc bd |
| a c |
3 2
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : M|N
o4 = | a d d2 ad |
| b e bc bd |
| c f a c |
3 4
o4 : Matrix R <--- R</pre>
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<h2>concatenate vertically</h2>
Use <a href="__vb_vb.html" title="a binary operator, often used for vertical concatenation">||</a> to concatenate two matrices vertically.<table class="examples"><tr><td><pre>i5 : P = matrix{{d^2,a*d,e*f},{b*c,b*d,b*e},{a,c,d}}
o5 = | d2 ad ef |
| bc bd be |
| a c d |
3 3
o5 : Matrix R <--- R</pre>
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<tr><td><pre>i6 : transpose(M)||P
o6 = {-1} | a b c |
{-1} | d e f |
{0} | d2 ad ef |
{0} | bc bd be |
{0} | a c d |
5 3
o6 : Matrix R <--- R</pre>
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<h2>making block matrices</h2>
The matrix function can take matrices as input as long as the sizes match up.<table class="examples"><tr><td><pre>i7 : matrix{{id_(R^3),M,P},{random(R^1,R^3),random(R^1,R^3),random(R^1,R^2)}}
o7 = | 1 0 0 a d d2 ad ef |
| 0 1 0 b e bc bd be |
| 0 0 1 c f a c d |
| -14215 14276 -9343 -2513 9387 -6475 -11220 14456 |
4 8
o7 : Matrix R <--- R</pre>
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Also, the number input entries in each row must be equal. It might seem like we could form the same matrix with the input <tt>matrix{{id_(R^3),M,P},{random(R^1,R^8)}}</tt> since <tt>random(R^1,R^8)</tt> will construct a 1 by 8 matrix that has the same number of columns as matrix <tt>matrix{{id_(R^3),M,P}}</tt> but as input into the matrix function that row entry must have 3 entries.<h2>direct sum of matrices as maps between modules</h2>
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