Chapter 16
The Singular Value Decomposition
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.
Figure 16.1
Image compression: a method that uses the SVD. Far left: original image; ...
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