The largest singular value of eXA0e-X is convex on convex sets of commuting matrices

Renan Sezer Sezginer; Michael L. Overton

doi:10.1109/9.45196

The largest singular value of eXA0e-X is convex on convex sets of commuting matrices

Renan Sezer Sezginer, Michael L. Overton

Research output: Contribution to journal › Article › peer-review

Abstract

A short and direct proof is given for the convexity of the largest singular value of eXA0e-X on any convex set of commuting matrices in Rnxn, where A0, Rnxn is fixed. This statement does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices.

Original language	English (US)
Pages (from-to)	229-230
Number of pages	2
Journal	IEEE Transactions on Automatic Control
Volume	35
Issue number	2
DOIs	https://doi.org/10.1109/9.45196
State	Published - Feb 1990

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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abstract = "A short and direct proof is given for the convexity of the largest singular value of eXA0e-X on any convex set of commuting matrices in Rnxn, where A0, Rnxn is fixed. This statement does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices.",

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AB - A short and direct proof is given for the convexity of the largest singular value of eXA0e-X on any convex set of commuting matrices in Rnxn, where A0, Rnxn is fixed. This statement does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices.

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The largest singular value of eXA0e-X is convex on convex sets of commuting matrices

Abstract

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