ABSTRACT
Matrix decomposition is a fundamental tool in linear algebra for understanding the action of a matrix, establishing its suitability to solve a problem, and for solving linear systems more efficiently and effectively. We have encountered an important decomposition already, the eigendecomposition for symmetric matrices (see Section 7.5). The topic of this chapter, the singular value decomposition (SVD), is a tool for more general, even nonsquare matrices. Figure 16.1 demonstrates one application of SVD, image compression. This chapter allows us to revisit several themes from past chapters:
eigenvalues and eigenvectors, the condition number, the least squares solution to an overdetermined system, and more! It provides a good review of some important ideas in linear algebra.
