# Weak interlacing properties of totally positive matrices

@article{Friedland1985WeakIP,
title={Weak interlacing properties of totally positive matrices},
author={Shmuel Friedland},
journal={Linear Algebra and its Applications},
year={1985},
volume={71},
pages={95-100}
}
• S. Friedland
• Published 1 November 1985
• Mathematics
• Linear Algebra and its Applications
14 Citations
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.
Interlacing Inequalities for Totally Nonnegative
• Mathematics
• 2000
Suppose 1 n 0 are the eigenvalues of an n n totally nonnegative matrix, and ~ 1 ~ k are the eigenvalues of a k k principal submatrix. A short proof is given of the interlacing inequalities: j are
Eigenvalues of products of matrices and submatrices in certain positivity classes
• Mathematics
• 2000
If A and B are n-by-n, positive semidefinite Herimitian matrices, then for any φ≠α⊆{1,2,… n}. A certain converse is given, as well as analogs for the product of several m-matrices and totally
An inverse eigenvalue problem for totally nonnegative matrices
In a previous paper we proved that the diagonal elements of a totally nonnegative matrix are majorized by its eigenvalues. In this note we show that the majorization of a vector of nonnegative real
An Interlacing Property of Eigenvalues ofStrictly Totally Positive
We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive matrices. x1. Introduction The central results concerning eigenvalues and eigenvectors
Spectral Structures of Irreducible Totally Nonnegative Matrices
• Mathematics
SIAM J. Matrix Anal. Appl.
• 2000
This work defines a notion of "principal rank" and employs this idea throughout to characterize all possible Jordan canonical forms (Jordan structures) of irreducible totally nonnegative matrices of n-by-n matrices.

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An inverse eigenvalue problem for totally nonnegative matrices
In a previous paper we proved that the diagonal elements of a totally nonnegative matrix are majorized by its eigenvalues. In this note we show that the majorization of a vector of nonnegative real
Extremal eigenvalue problems for convex sets of symmetric matrices and operators
LetA1,...,An andK bem×m symmetric matrices withK positive definite. Denote byC the convex hull of {A1,...An}. Let {λp(KA)}1n be then real eigenvalues ofKA arranged in decreasing order. We show that
The Hadamard-Fischer inequality for a class of matrices defined by eigenvalue monotonicity
• Mathematics, Philosophy
• 1976
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