The Matrix of An Endomorphism
An important case of the matrix of a linear transformation is that of an endomorphism, that is, a linear map from a vector space V to itself: that is, the case that W = V. We can naturally take {β1, ..., βn} = {α1, ..., αn} and {β'1, ..., β'm} = {α'1, ..., α'n}. The matrix of the linear map T is necessarily square.
Read more about this topic: Change Of Basis
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