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

The interlacing theorem of Cauchy–Poincaré states that the eigenvalues of a principal submatrix A0 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–Poincaré and Fan–Pall interlacing theorems for J-Hermitian and J-normal matrices. The corresponding inverse spectral problems are also considered.