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