Spectral variation of normal matrices

Spectral Variation, Normal Matrices, and Finsler Geometry

Spectral Variation Bounds for Diagonalisable Matrices

This note is related to an earlier paper by Bhatia, Davis, and Kittaneh 4]. For matrices similar to Hermitian, we prove an inequality complementary to the one proved in 4, Theorem 3]. We also disprove a conjecture made in 4] about the norm of a commutator.

Convergence of the Spectral Measure of Non-normal Matrices

We discuss regularization by noise of the spectrum of large random non-normal matrices. Under suitable conditions, we show that the regularization of a sequence of matrices that converges in ∗-moments to a regular element a by the addition of a polynomially vanishing Gaussian Ginibre matrix forces the empirical measure of eigenvalues to converge to the Brown measure of a.

Matrices, Jordan Normal Forms, and Spectral Radius Theory

Matrix interpretations are useful as measure functions in termination proving. In order to use these interpretations also for complexity analysis, the growth rate of matrix powers has to examined. Here, we formalized an important result of spectral radius theory, namely that the growth rate is polynomially bounded if and only if the spectral radius of a matrix is at most one. To formally prove ...

Spectral operators of matrices

The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool to model many important applications involving structured low rank matrices within and beyond the optimization community. This trend can be credited to some extent to the exciting developments in emerging fields such as compressed sensing. The Löwner operator, which generates a matrix valu...