Some interlacing results for indefinite Hermitian matrices
A classical theorem states that the eigenvalues of a principal submatrix of deficiency one of a Hermitian matrix interlace the eigenvalues of the full matrix. The authors consider the similar situation when the underlying inner product is no longer definite. Interlacing no longer holds, eigenvalues may be complex, and the structure of Jordan chains must be considered. In spite of this intricacy there are nontrivial facts concerning the location of the spectrum of the submatrix relative to that of the full matrix. These are too intricate to reproduce here. \{The reviewer's paper, ibid. 14, 135--177 (1976; Zbl 0386.15011) uses a simultaneous reduction for two Hermitian matrices to study similar questions and should be added to the references.\}
scientific article; zbMATH DE number 3922871