Bordering for spectrally arbitrary sign patterns

We develop a matrix bordering technique that can be applied to an irreducible spectrally arbitrary sign pattern to construct a higher order spectrally arbitrary sign pattern. This technique generalizes a recently developed triangle extension method. We describe recursive constructions of spectrally...

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Veröffentlicht in:Linear algebra and its applications 2017-12, Vol.534, p.36-50
Hauptverfasser: Olesky, D.D., van den Driessche, P., Vander Meulen, K.N.
Format: Artikel
Sprache:eng
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Zusammenfassung:We develop a matrix bordering technique that can be applied to an irreducible spectrally arbitrary sign pattern to construct a higher order spectrally arbitrary sign pattern. This technique generalizes a recently developed triangle extension method. We describe recursive constructions of spectrally arbitrary patterns using our bordering technique, and show that a slight variation of this technique can be used to construct inertially arbitrary sign patterns.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.08.006