Matrix Polynomials and Canonical Forms

Abstract

This chapter is devoted to matrix decompositions. The main studies are on the Schur decomposition, spectral decomposition, singular value decomposition, Jordan decomposition, and numerical range. Attention is also paid to the polynomials that annihilate matrices, especially the minimal and characteristic polynomials, and to the similarity of a complex matrix to a real matrix. At the end we introduce three important matrix operations: the Hadamard product, the Kronecker product, and compound matrices.