Generating potentially nilpotent full sign patterns

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In-Jae Kim
Dale D. Olesky
Bryan L. Shader
Pauline van den Driessche
Hein van der Holst
Kevin N. Vander Meulen


A sign pattern is a matrix with entries in {+,−, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns that are not full, as well as potentially stable sign patterns.

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