Abstract In this article, a generalized Schur complement defined by the Moore-Penrose inverse and *congruence to a Hermitian block matrix are studied for a generalization of Haynsworth’s theorem. As an application, an alternative proof of Albert’s characterization of positivity is obtained A. Albert, SIAM J. Appl. Math. (1969). Some of our results of matrices are extended to bounded linear operators.
Takashi Sano (Fri,) studied this question.