On perturbations of matrix pencils with real spectra. II
Rajendra Bhatia, Ren‐Cang Li · Mathematics of Computation · 1996
A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A A and A ~ \widetilde A be two n × n n\times n Hermitian matrices, and let λ 1 \lambda _1 , …, λ n \lambda _{n} and λ ~ 1 \widetilde \lambda _1 , …, λ ~ n \widetilde \lambda _{n} be their eigenvalues arranged in ascending order. Then ⦀ diag ( λ 1 − λ ~ 1 , … , λ n − λ ~ n )