Sets of refined inertias of zero–nonzero patterns

A set Hn⁎ of refined inertias for zero–nonzero patterns is introduced that is analogous to the set Hn previously considered for sign patterns. For n=3 and 4, a complete characterization of irreducible zero–nonzero patterns that allow or require Hn⁎ is given, and each zero–nonzero pattern that allows...

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Veröffentlicht in:Linear algebra and its applications 2017-03, Vol.516, p.243-263
Hauptverfasser: Berliner, Adam H., Olesky, D.D., van den Driessche, P.
Format: Artikel
Sprache:eng
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Zusammenfassung:A set Hn⁎ of refined inertias for zero–nonzero patterns is introduced that is analogous to the set Hn previously considered for sign patterns. For n=3 and 4, a complete characterization of irreducible zero–nonzero patterns that allow or require Hn⁎ is given, and each zero–nonzero pattern that allows Hn⁎ has a signing that allows Hn. In contrast, for n≥5 a family of irreducible zero–nonzero patterns is given that allows Hn⁎ but for which no one signing allows Hn.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.11.040