Journal or Book Title
Linear and Multilinear Algebra
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.
Taylor & Francis
Hogben, Leslie; Lin, Jephian C.-H.; Olesky, D. D.; and van den Driessche, P., "The sepr-sets of sign patterns" (2020). Mathematics Publications. 208.