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.
Copyright Owner
Taylor & Francis
Copyright Date
2019
Language
en
File Format
application/pdf
Recommended Citation
Hogben, Leslie; Lin, Jephian C.-H.; Olesky, D. D.; and van den Driessche, P., "The sepr-sets of sign patterns" (2020). Mathematics Publications. 208.
https://lib.dr.iastate.edu/math_pubs/208
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.