An extremal problem for positive defintie matrices

1 January 1978

journal article
research article
Published by Taylor & Francis in Linear and Multilinear Algebra

Vol. 6 (4) , 257-262
https://doi.org/10.1080/03081087808817247

Abstract

A problem studied by Flanders (1975) is minimize the function f(R)=tr(SR+TR ⁻¹) over the set of positive definite matrices R, where S and T are positive semi-definite matrices. Alternative proofs that may have some intrinsic interest are provided. The proofs explicitly yield the infimum of f(R). One proof is based on a convexity argument and the other on a sequence of reductions to a univariate problem.

Keywords

DEFINTIE MATRICES
POSITIVE DEFINTIE
EXTREMAL PROBLEM
DEFINITE MATRICES
PROBLEM STUDIED
FLANDERS
ARGUMENT

This publication has 2 references indexed in Scilit:

An extremal problem on the space of positive definite matrices
Linear and Multilinear Algebra, 1975
Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators
Proceedings of the National Academy of Sciences, 1951