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 |
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Section MR | Matrix Representations |

Section CB | Change of Basis |

Section OD | Orthonormal Diagonalization |