Trace class multipliers and spectral variation of normal matrices

Spectral Variation, Normal Matrices, and Finsler Geometry

Trace formula and Spectral Riemann Surfaces for a class of tri-diagonal matrices

For tri-diagonal matrices arising in the simplified Jaynes– Cummings model, we give an asymptotics of the eigenvalues, prove a trace formula and show that the Spectral Riemann Surface is irreducible.

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.

Estimating the spectral gap of a trace-class Markov operator

The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating) the spectral gaps of practical Monte Carlo Markov chains in statistics has proven to be an extremely difficult and often insurmountable task, especially when these chains move on continuous state spa...

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 ...