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<p>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.</p>

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Moore-Penrose inverse, generalized Schur complement and inertia

  • 期刊论文

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  • 发表日期：

    2026年2月27日

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  • Takashi Sano

摘要

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.