Generating potentially nilpotent full sign patterns

Generating potentially nilpotent full sign patterns

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...

Potentially nilpotent tridiagonal sign patterns of order 4

Nilpotent matrices and spectrally arbitrary sign patterns

It is shown that all potentially nilpotent full sign patterns are spectrally arbitrary. A related result for sign patterns all of whose zeros lie on the main diagonal is also given.

Potentially eventually positive double star sign patterns

In this work, the potentially eventually positive double star sign patterns are characterized. It is shown that, up to equivalence, an (m + n) × (m + n) double star sign pattern is potentially eventually positive if and only if it is a superpattern of four specific sign patterns. © 2012 Elsevier Ltd. All rights reserved.

Potentially eventually exponentially positive sign patterns

We introduce the study of potentially eventually exponentially positive (PEEP) sign patterns and establish several results using the connections between these sign patterns and the potentially eventually positive (PEP) sign patterns. It is shown that the problem of characterizing PEEP sign patterns is not equivalent to that of characterizing PEP sign patterns. A characterization of all 2× 2 and...