The Variation Of The Spectrum Of A Block Upper Triangular Matrix

In this paper we investigate the matrix perturbation analysis of eigenvalue perturbation theory. Applying previous results, some new perturbation bounds are presented for block upper triangular matrix and reducible matrix. These bounds improved the previous results on the perturbation of the eigenvalue.The first chapter is the introduction. In this chapter, we introduce background of the matrix perturbation analysis, and give overview of this article.In chapter2we describe some important conceptions and theorems in the matrix perturbation analysis.Chapter3focuses on the block upper triangular matrix eigenvalue. Block upper triangular matrix has an important significance in practice. In this chapter we studies the Euclid distance of spectrum of two matrices.In chapter4we introduce reducible matrix perturbation bounds. We discuss the variation of the spectrum of two reducible matrices.Finally, there is the conclusion of this article. We show that our results improved the previous results on the perturbation of the eigenvalue and we study the prospects for the development of content.