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A Matricial Proof of the Symmetric Exchange Axiom for Eigenvalues of Principal Submatrices of a Complex Hermitian Matrix

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
438
Issue
9
Identifiers
DOI: 10.1016/j.laa.2013.01.006
Keywords
  • 15A15
  • 15A18
  • 15A29
  • Hermitian Matrices
  • Submatrices
  • Eigenvalues
  • Symmetric Exchange Axiom

Abstract

Abstract In [C.R. Johnson, B. Kroschel, M. Omladič, Eigenvalue multiplicities in principal submatrices, Linear Algebra Appl. 390 (2004) 111-120] a result constraining the eigenvalues of principal submatrices of complex Hermitian matrices, based upon matroid theory, was given. Here we give a matricial proof of this result which also enables us to find a generalization of the original result.

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