Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

2020

Journal or Book Title

Linear and Multilinear Algebra

Volume

68

Issue

10

First Page

2044

Last Page

2068

DOI

10.1080/03081087.2019.1570067

Abstract

Given a real symmetric n×n matrix, the sepr-sequence t1⋯tn records information about the existence of principal minors of each order that are positive, negative, or zero. This paper extends the notion of the sepr-sequence to matrices whose entries are of prescribed signs, that is, to sign patterns. A sufficient condition is given for a sign pattern to have a unique sepr-sequence, and it is conjectured to be necessary. The sepr-sequences of sign semi-stable patterns are shown to be well-structured; in some special circumstances, the sepr-sequence is enough to guarantee that the sign pattern is sign semi-stable. In alignment with previous work on symmetric matrices, the sepr-sequences for sign patterns realized by symmetric nonnegative matrices of orders two and three are characterized.

Comments

This is an Accepted Manuscript of an article published by Taylor & Francis as Hogben, Leslie, Jephian C.-H. Lin, D. D. Olesky, and P. van den Driessche. "The sepr-sets of sign patterns." Linear and Multilinear Algebra 68, no. 10 (2020): 2044-2068. DOI: 10.1080/03081087.2019.1570067. Posted with permission.

Copyright Owner

Taylor & Francis

Language

en

File Format

application/pdf

Published Version

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