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Analogs of Cauchy-Poincare and Fan-Pall interlacing theorems for J-Hermitian and J-normal matrices

Authors: Bebiano N, Furtado S, da Providencia J

Ref.: LINEAR ALGEBRA AND ITS APPLICATIONS 433, 80 (2010)

Abstract: The interlacing theorem of Cauchy-Poincare states that the eigenvalues of a principal submatrix A(0) of a Hermitian matrix A interlace the eigenvalues of A. Fan and Pall obtained an analog of this theorem for normal matrices. In this note we investigate analogs of Cauchy-Poincare and Fan-Pall interlacing theorems for J-Hermitian and J-normal matrices. The corresponding inverse spectral problems are also considered.