Eigenvalues and Singular Values

In this chapter, the authors discuss some of the properties (eigenvectors and eigenvalues) of matrices and concentrate on square matrices. They discuss singular value decomposition and generalize the results for both square and nonsquare matrices. The authors introduce the application of eigenvalues and eigenvectors in matrix diagonalization including some important properties of matrices. Diagonalization of a matrix generally reduces computational overhead, e.g. numerical optimization. The authors present an approach that is general enough to be applied for diagonalization of all matrices. A large condition number means that the matrix is ill‐conditioned. Control of ill‐conditioned plants is difficult, as some combinations of the inputs have a strong effect on the outputs, whereas other combinations have a weak effect on the outputs.