Title

Eigenvalue Multiplicities in Principal Submatrices

Department/School

Mathematics

Date

1-1-2004

Document Type

Article

Keywords

Eigenvalues, geometric multiplicity, principal submatrices

DOI

https://doi.org/10.1016/j.laa.2004.04.019

Abstract

Let λ be an eigenvalue of an n-by-n matrix A. The allowable patterns of geometric multiplicities of λ as an eigenvalue of A and its principal submatrices is explored. A graphical hierarchy for succinctly reporting the possible patterns is defined. Special attention is paid to the case in which A is Hermitian. Classical interlacing already imposes much structure on the hierarchies in the Hermitian case. Here, all the known constraints, some old and some new, on the geometric multiplicity hierarchies of Hermitian matrices are listed. Some differences between allowed hierarchies for real symmetric matrices and Hermitian matrices are also discussed.

Published in

Linear Algebra and Its Applications

Citation/Other Information

Johnson, C. R., Kroschel, B. K., & Omladič, M. (2004). Eigenvalue multiplicities in principal submatrices. Linear Algebra and Its Applications, 390, 111–120. https://doi.org/10.1016/j.laa.2004.04.019

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