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arXiv · 1611.08217

Refined Inertia of Matrix Patterns

Jonathan Earl·Kevin N. Vander Meulen·Adam Van Tuyl
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Abstract

We explore how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. We demonstrate that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike what happens for nonzero patterns. We develop a class of patterns that are refined inertially arbitrary but not spectrally arbitrary, making use of the property of a properly signed nest. We include a characterization of the inertially arbitrary and refined inertially arbitrary patterns of order three, as well as the patterns of order four with the least number of nonzero entries.

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Jonathan Earl, Kevin N. Vander Meulen, Adam Van Tuyl. 2016-11-24. Refined Inertia of Matrix Patterns. https://arxiv.org/abs/1611.08217

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