Notes on ω- and τ-matrices

  title={Notes on $\omega$- and $\tau$-matrices},
  author={Daniel Hershkowitz and Abraham Berman},
  journal={Linear Algebra and its Applications},
On some conjectures on the spectra of τ-matrices
We will consider three conjectures of Schneider and Varga concerning the location of eigenvalues of ω- and τ-matices in the complex plane, and extend the known results to n ⩽ 4. We will further show
Theorems and counterexamples on structured matrices
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation.
R A ] 5 S ep 2 00 1 Open problems on GKK τ-matrices
Several open problems on GKK τ -matrices raised by examples showing that some such matrices are unstable are proposed.
Open Problems on Gkk -Matrices
Several open problems on GKK -matrices raised by examples showing that some such matrices are unstable are proposed.
PII: S0024-3795(01)00492-X
We propose several open problems on GKK τ -matrices raised by examples showing that some such matrices are unstable. © 2002 Elsevier Science Inc. All rights reserved. AMS classification: 15A15;
R A ] 2 7 D ec 2 00 5 Not all GKK τ-matrices are stable
Hermitian positive definite, totally positive, and nonsingular M -matrices enjoy many common properties, in particular (A) positivity of all principal minors, (B) weak sign symmetry, (C) eigenvalue


Matrix Diagonal Stability and Its Implications
Relations between diagonal stability, stability, positiveness of principal minors and semipositivity are described for several classes of matrices. In particular, it is shown that for matrices whose
On complex eigenvalues ofM andP matrices
SummaryInequalities are obtained for the complex eigenvalues of anM matrix or aP matrix which depend only on the order of the matrix.
Necessary conditions and a sufficient condition for the Fischer-Hadamard inequalities
It is well known that a matrix, all of whose principal minors are positive, satisfies the Fischer-Hadamard inequalities if and only if it is weakly sign symmetric. In this paper we consider the
Analytic functions of M-matrices and generalizations
We introduce the notion of positivity cone K of matrices in and with such a K we associate sets Z and M. For suitable choices of K the set M consists of the classical (non-singular) M-matriccs or of
Oscillation matrices and kernels and small vibrations of mechanical systems
Introduction Review of matrices and quadratic forms Oscillatory matrices Small oscillations of mechanical systems with $n$ degrees of freedom Small oscillations of mechanical systems with an infinite
The Hadamard-Fischer inequality for a class of matrices defined by eigenvalue monotonicity
1) Spec A[Jl.l n IR =1= t/>, for t/> c Jl. S (n), 2) I(A[J-L]) « I(A[v]), if t/> c v S Jl. S (n), where I(A[Jl.]) = min(Spec A[Jl.l n IR). For A, BE W(n), define A «, B by I(A[J-L]) « I(B[J-L]), for