A note on sign patterns of order 3 that require particular refined inertias

作者：Garnett C; Olesky D D^*; van den Driessche P

来源：Linear Algebra and Its Applications, 2014, 450: 293-300.

DOI：10.1016/j.laa.2014.03.007

• Sign pattern
• Refined inertia
• Eigenvalues

For a real n x n matrix A having n(+) (n(-_)) eigenvalues with positive (resp. negative) real part, n(z) zero eigenvalues and 2n(p), nonzero pure imaginary eigenvalues, the refined inertia of A is ri(A) = (n(+), n(-), n(z), 2n(p)). When n = 3, let H-3 = {(0, 3, 0, 0), (0, 1, 0, 2), (2, 1, 0, 0)}. A 3 x 3 sign pattern A requires refined inertia H-3 if {ri(A) | A has sign pattern A} = H-3. Necessary and sufficient conditions for an irreducible sign pattern to require H-3 are given, and used to determine all such sign patterns (up to equivalence). These remove equivalences and complete the list of patterns given in [1, Appendix A].

• 出版日期2014-6-1