The Singular Value Decomposition

The kind of method of moments (MoM) used in this chapter is based on point matching in both spatial and frequency domains. The singular value decomposition (SVD) of a rectangular matrix is introduced in the chapter as an extension of the basic theory of the eigenvalues and eigenvectors of a square matrix. So, preliminarily, some reminders about the eigenvalues and eigenvectors are provided in relationship to matrix inversions. The problem of solving rectangular linear algebraic systems can be dealt with in a regularized way, which requires an extension of the eigenvalue theory; this extension is the SVD. The SVD provides not only a method for the solution of the problem but also a possible method for the analysis the problem. In particular, even if numerically, the SVD can help us to understand the characteristics of the scattering operator.