Previous work with linear transformations may have convinced you that we can convert most questions about linear transformations into questions about systems of equations or properties of subspaces of $\complex{m}$. In this section we begin to make these vague notions precise. We have used the word “representation” prior, but it will get a heavy workout in this chapter. In many ways, everything we have studied so far was in preparation for this chapter.

Section VR Vector Representations
Section MR Matrix Representations
Section CB Change of Basis
Section OD Orthonormal Diagonalization