Some interlacing properties of the Schur complement of a Hermitian matrix.(English)Zbl 0765.15007

The author presents the following result: — It is shown for a Hermitian matrix $$H$$ with nonsingular principal submatrix $$A$$, that the eigenvalues of the Moore-Penrose inverse of the Schur complement $$(H/A)$$ of $$A$$ in $$H$$ interlace the eigenvalues of the Moore-Penrose inverse of $$H$$. Also, if $$H$$ is semidefinite, then the eigenvalues of $$(H/A)$$ interlace the eigenvalues of $$H$$.