Sums of real parts of eigenvalues of perturbed matrices

on direct sums of baer modules

the notion of baer modules was defined recently

Eigenvalues of sums of pseudo-Hermitian matrices

We study analogues of classical inequalities for the eigenvalues of sums of Hermitian matrices for the cone of admissible elements in the pseudo-Hermitian case. In particular, we obtain analogues of the Lidskii-Wielandt inequalities.

Ela Eigenvalues of Sums of Pseudo-hermitian Matrices

We study analogues of classical inequalities for the eigenvalues of sums of Hermitian matrices for the cone of admissible elements in the pseudo-Hermitian case. In particular, we obtain analogues of the Lidskii-Wielandt inequalities.

Parallel Computation of Eigenvalues of Real Matrices

A Note on Eigenvalues of Perturbed Hermitian Matrices

Let A = ( H1 E ∗ E H2 ) and à = ( H1 O O H2 ) be Hermitian matrices with eigenvalues λ1 ≥ · · · ≥ λk and λ̃1 ≥ · · · ≥ λ̃k, respectively. Denote by ‖E‖ the spectral norm of the matrix E, and η the spectral gap between the spectra of H1 and H2. It is shown that |λi − λ̃i| ≤ 2‖E‖ η + √ η2 + 4‖E‖2 , which improves all the existing results. Similar bounds are obtained for singular values of matrices u...