In Chap. 4 we learned how to diagonalize a square matrix using the Eigen decomposition. Eigen decomposition has many uses, but it has a limitation: it can only be applied to a square matrix. In this chapter, we will learn how to extend the decomposition to a rectangular matrix using a related method known as a Singular Value Decomposition (SVD). Because of its flexibility and numerical accuracy, the SVD is arguably the most useful decomposition ever developed. In fact, it’s probably fair to say that if you were stuck on an island with only one tool for performing linear algebra, you’d want the SVD.
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