Dale Olesky

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 arbitrary patterns using our bordering technique, and show that a slight variation of this technique can be used to construct inertially arbitrary sign patterns.