# Notes on ω- and τ-matrices

@article{Hershkowitz1984NotesO,
title={Notes on $\omega$- and $\tau$-matrices},
author={Daniel Hershkowitz and Abraham Berman},
journal={Linear Algebra and its Applications},
year={1984},
volume={58},
pages={169-183}
}
• Published 1 April 1984
• Physics
• Linear Algebra and its Applications
12 Citations
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
• Philosophy
• 2002
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

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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