1. The sepr-sets of sign patterns.
- Author
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Hogben, Leslie, Lin, Jephian C.-H., Olesky, D.D., and van den Driessche, P.
- Subjects
- *
SYMMETRIC matrices , *NONNEGATIVE matrices , *MATRICES (Mathematics) , *MINORS - Abstract
Given a real symmetric n × n matrix, the sepr-sequence t 1 ⋯ t n 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. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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