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.
Available at: http://works.bepress.com/leslie-hogben/91/
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.