On perturbations of matrix pencils with real spectra. II

Abstract

A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and à be two nxn Hermitian matrices, and let λ₁,...,λ_n and λ₁,...,λ_n be their eigenvalues arranged in ascending order. Then diag |||(λ₁-λ₁,...,λ_n-λ_n) ≤|||A-Ã||| for any unitarily invariant norm ||| .|||. In this paper, we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra. The much studied case of definite pencils is included in this.