Matrix Perturbation Of A Number Of Issues

In the chapters 2 and 3 in this paper, the Hoffmam - Wieldant bounds for additive and multiplicative perturbations are discussed. It is mainly studied diagonalizable (see 2.1,2.3, 3.1, 3.2) and arbitrary (see 2.2) matrix perturbations. In the fourth chapter we deal with the eigenspace (see 4.1) and singular space (see 4.2) perturbations. Lastly we consider the perturbation bound on Hermitian positive semidefinte factors for unitrary polar decomposition (see 5.1), which'improve and extend the corresponding results in other papers.