| In this paper,we discuss the perturbation of matrixeigenvalues associated with invariant subspaces and relativeperturbation of matrix eigenvalues. Some new perturbationbounds are presented. We systematically studied the perturbation of matrixeigenvalues associated with invariant subspaces. Some newHoffman-Wielandt type bounds on the variations betweeneigenvalues of two diagonalisable matrixes associated withinvariant subspaces are obtained . Some Weyl type bounds areobtianed also. Perturbation of eigenvalues of more generalmatrix is also studied. First,we improve some theroies. Using the invariation ofthe eigenvalues of two matrixes if one matrix is similar toanother,we extend Bauer-Fike type relative perturbationtheory and obtain a new relative perturbation bound foreigenvalues of diagonalisable matrix.Using hyperbolicsingular decompositon to study perturbation for eigenvaluesof indefinte Hermite matrix have some development,we use somenew methods to get some new relative perturbation bounds. |
