Title

The critical exponent for continuous conventional powers of doubly nonnegative matrices

Document Type

Article

Department/Program

Mathematics

Journal Title

Linear Algebra and Its Applications

Pub Date

2011

Volume

435

Issue

9

First Page

2175

Abstract

We prove that there exists an exponent beyond which all continuous conventional powers of n-by-n doubly nonnegative matrices are doubly nonnegative. We show that this critical exponent cannot be less than n - 2 and we conjecture that it is always n - 2 (as it is with Hadamard powering). We prove this conjecture when n < 6 and in certain other special cases. We establish a quadratic bound for the critical exponent in general. (C) 2011 Elsevier Inc. All rights reserved.

DOI

10.1016/j.laa.2010.08.046

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