ABSTRACT
The purpose of this chapter is to re-interpret some of the main results of the book in terms of matrix factorizations. We have already encountered several factorizations: the spectral decomposition of a square, diagonalizable matrix, the Jordan canonical form of a general square matrix, and the singular value decomposition of a general (not necessarily square) matrix. The factorizations (or decompositions) express concisely the eigenvalue-eigenvector relationships and allow convenient manipulations that take advantage of these relationships.
