Theoretical Mathematics & Applications

Study of Partitioned Operators and Its Applications

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  • Abstract

    In this paper, we find new properties of Partitioned matrices, and some new relations between Positive semidefinite matrices and Hermitian block, and we give necessary and sufficient conditions for a partitioned operator matrix to have the Drazin inverse with Banachiewicz–Schur.

    Mathematics Subject Classifications: 15A18; 15A60; 26C10; 30C15
    Keywords: Determent; nilpotent; Positive definite matrices; Hermitian matrix; Schur complement; Drazin inverse