Mathematics Faculty Articles

Title

An Analytic Approach To a Permanent Conjecture

Document Type

Article

Publication Date

2-1-2013

Publication Title

Linear Algebra and its Applications

Keywords

Hadamard product, Irreducible matrix, Lagrange multiplier, Maximizing matrix, Permanent

ISSN

0024-3795

Volume

438

Issue/No.

4

First Page

1570

Last Page

1579

Abstract

This paper is concerned with the conjecture on the permanent of the Hadamard product of two positive semidefinite matrices: per(A∘B)≼perAperB. We present some properties of correlation matrices and introduce an analytic approach of maximizing matrices for the permanent conjecture. Given an irreducible correlation matrix, we show that its maximizing matrix is (i) singular, (ii) irreducible, and (iii) invariant by a row and column reduction.

DOI

10.1016/j.laa.2011.09.034

Peer Reviewed

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