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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_matrices.html" title="">matrices</a> > <a href="_inputting_spa_spmatrix.html" title="">inputting a matrix</a></div>
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<div><h1>inputting a matrix</h1>
<div><h2>by its entries</h2>
Using the function <a href="_matrix.html" title="make a matrix">matrix</a> is the most basic method for inputting a matrix. The entries are typed in by rows.<table class="examples"><tr><td><pre>i1 : R = ZZ/5[s..z];</pre>
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<tr><td><pre>i2 : M = matrix {{ x^2+y, z^3}, {y^3-z,3*z-6*x-5*y}}
o2 = | x2+y z3 |
| y3-z -x-2z |
2 2
o2 : Matrix R <--- R</pre>
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<h2>by a function</h2>
The function <a href="_map.html" title="make a map">map</a> can be used to construct matrices. <table class="examples"><tr><td><pre>i3 : G = map(R^3,3,(i,j)->R_i^j)
o3 = | 1 s s2 |
| 1 t t2 |
| 1 u u2 |
3 3
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : f = 3*s^2*v-t*u*v+s*t^2
2 2
o4 = s*t - 2s v - t*u*v
o4 : R</pre>
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<tr><td><pre>i5 : H = map(R^4,R^4,(i,j)->diff(R_j*R_i,f))
o5 = | v 2t 0 s |
| 2t 2s -v -u |
| 0 -v 0 -t |
| s -u -t 0 |
4 4
o5 : Matrix R <--- R</pre>
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<h2>identity matrix</h2>
The function <a href="_id.html" title="identity map">id</a> is used to form the identity matrix as a map from a module to itself. <table class="examples"><tr><td><pre>i6 : id_(R^3)
o6 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
3 3
o6 : Matrix R <--- R</pre>
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<tr><td><pre>i7 : id_(source M)
o7 = {3} | 1 0 |
{3} | 0 1 |
2 2
o7 : Matrix R <--- R</pre>
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The first example gives a 3x3 identity matrix with entries in the ring R. The second gives a 2x2 identity matrix whose source and target are the (graded) source of the matrix <tt>M</tt>.</div>
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