Perturbation Bounds Of Polar Factors In The Polar Decomposition And Perturbation Bounds For The Eigenvalues Of A Singular Diagonalizable Matrix

The problem of matrix perturbation has profound theoretical significance and the broad application background. Let f be a map from M into R, where M is the set of matrices. The central question of perturbation theory for the map f should be as follows: How does f(A) change when A is subject to perturbation. The problems of matrix perturbation not only come from engineering technology, but also appear in some pure mathematics problems. In this paper, the following main works are given.In Chapter 1, we introduce the research background of the problem and the main content of this paper.In Chapter 2, some important conceptions and theories in the matrix perturbation analysis are introduced.In Chapter 3, some important conceptions in the polar decomposition of matrix are introduced. The multiplicative perturbation bounds and the additive perturbation bounds of the (sub)unitary polar factor for the generalized polar decomposition are given. Some new perturbation bounds are presented, which improve the previous bounds.In Chapter 4, the perturbation bounds for the eigenvalues of a singular diagonalizable matrix are investigated, which are better than the existing bounds in some sense.