Some interlacing properties of the Schur complement of a Hermitian matrix

Abstract For a Hermitian matrix H with nonsingular principal submatrix A, it is shown 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. Moreover, if H is semidefinite, it is shown that the eigenvalues of (H/A) interlace the eigenvalues of H.

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