The Study Of Perturbation Bounds For Matric Elgenvalues

The purpose of this paper is to study the additive perturbation and multiplicative perturbation of the matrix eigenvalues. Applying matrix singular value decomposition and polar decomposition perturbation to analysis a class of matrix and its extended matrix eigenvalue.Some new absolute perturbation bounds of matrix are obtained.In the first chapter, the current study situation and basic knowledge of matrix eigenvalues are introduced and made a total description of some of the important contents of this article.In the second chapter,some basic knowledge of the matrix eigenvalues are introduced.In the third chapter,applying the singular value decomposition, some new perturbation bounds of special matrix are obtained, that theorem3.2.1arid3.2.2where A,B are symmetrizable matrix, Norm inequalities applied to the spectrum of the Euclidean distance and get theorem3.2.3. Release of these conditions, extended to any matrix getting. theorem3.3.1.In the forth chapter, for the extended matrix and its first type of perturbation matrix, when the rank are not equal, using extended matrix singular value decomposition, the absolute perturbation bounds of singular space under non-preserving perturbation are deducted. That is theorem4.2.1At the same time the absolute perturbation bounds of positive semidefinite factor under non-preserving perturbation are deducted. That is theorem4.2.2In the fifth chapter, applying the singular value decomposition and polar decomposition of generalized extended matrix,some new perturbation bounds of the polar factor under addition perturbation are obtained,that, is theorem5.2.1, the perturbation bounds of the polar factor under multiplicative perturbation are obtained, hat, is theorem5.3.1.