Perturbation Analysis Of Matrix Eigenvalues

The purpose of this paper is to study the additive perturbation of matrix eigenvalues. Some new absolute and relative perturbation bounds of matrix are obtained.The details will go as follows:Firstly, the current study situation and basic knowledge of matrix eigenvalues are introduced.Secondly, we improve some previous corresponding results in some sense. Using the singular value decomposition ,some new Wielandt-Hoffman type and Weyl type absolute perturbation bounds of special matrix, symmetrizable matrix, diagonalizable matrix are obtained. We also analyze the arbitrary perturbation of normal matrix, based on we give Weyl type absolute perturbation bounds of normal matrix. Using the schur triangular factorization of matrix, we extend the absolute perturbation bounds of arbitrary matrix. We use some new methods to get results, which improve and extend the corresponding results in other papers.Lastly, the new relative perturbation bounds for special matrix and diagonalizable matrix are obtained. Using the schur triangular factorization of matrix, we deal with the relative perturbation bounds of arbitrary matrix and give some new theorems.