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<head><title>constructing maps between modules</title>
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<div><h1>constructing maps between modules</h1>
<div>Let's start with a free module.<table class="examples"><tr><td><pre>i1 : R = ZZ/5[x,y,z];</pre>
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<tr><td><pre>i2 : F = R^3
3
o2 = R
o2 : R-module, free</pre>
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A list of indices can be used to produce homomorphisms corresponding to the corresponding basis vectors.<table class="examples"><tr><td><pre>i3 : F_{0,1,2}
o3 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
3 3
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : F_{0,1}
o4 = | 1 0 |
| 0 1 |
| 0 0 |
3 2
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : F_{1,2}
o5 = | 0 0 |
| 1 0 |
| 0 1 |
3 2
o5 : Matrix R <--- R</pre>
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Matrices are viewed as linear transformations.<table class="examples"><tr><td><pre>i6 : f = matrix{{x,y,z}}
o6 = | x y z |
1 3
o6 : Matrix R <--- R</pre>
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