Throughout this chapter V, W are vector spaces over the same field F. We have seen that the matrix associated with a given linear transformation T: V→ W is dependent upon the bases chosen for V and W. Thus there are lots of such matrices: one corresponding to each choice of bases. It would be helpful for computational purposes if we knew how to make a particular choice of basis for which the associated matrix was as simple as possible. It is this objective that we have in mind in the current chapter.
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