Brève communication. Localisation de valeurs propres, régions de Gudkov
Brèves communications. Un corollaire du théorème de Perron-Frobenius
Cauchy's interlace theorem and lower bounds for the spectral radius.
Changes in signature induced by the Lyapunov mapping .
Comparison theorems for weak nonnegative splittings of -monotone matrices.
Concentration of the spectral measure for large random matrices with stable entries.
Concentration of the spectral measure of large Wishart matrices with dependent entries.
Convergence of -norms of a matrix
a recurrence relation for computing the -norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed.
Convex -invariant functions and refinements of von Neumann’s inequality
A function on which is -invariant is convex if and only if its restriction to the subspace of diagonal matrices is convex. This results from Von Neumann type inequalities and appeals, in the case where , to the notion of signed singular value.
Cyclic products and an inequality for determinants
Die Lösung der Matrizengleichung X - AXB = C durch Integration.
Directed forests with application to algorithms related to Markov chains
This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.
Eigenvalue frequency and consistent sign pattern matrices
Eigenvalues of Rayleigh quotient matrices.
Eigenvalues of sums of hermitian matrices
Eigenvalues of sums of pseudo-Hermitian matrices.
Eigenvectors of acyclic matrices
Eigenwertabschätzungen für Matrizen.
Eine Eigenwertabschätzung für Integraloperatoren mit stochastischen Kernen
Equality in Wielandt’s eigenvalue inequality
In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.