In this chapter, we shall develop another type of factorization, which is a generalization of the diagonalization procedure discussed in Chapter 18. This factorization is applicable to any real m × n matrix A, and in the literature has been named as the singular value decomposition (SVD). Besides solving linear systems, SVD has a wide variety of applications in diverse fields such as data compression, noise reduction, storage, estimating the rank of a matrix, and transmission of digitized information. Before we state the main result of this chapter, let us recall the following steps: