Formulae for the generalized Drazin inverse of a block matrix in terms of Banachiewicz–Schur forms
نویسندگان
چکیده
We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices.
منابع مشابه
Generalized Drazin inverse of certain block matrices in Banach algebras
Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.
متن کاملExpressions for the generalized Drazin inverse of a block matrix in a Banach algebra
We present some new representations for the generalized Drazin inverse of a block matrix with generalized Schur complement being generalized Drazin invertible in a Banach algebra under conditions weaker than those used in recent papers on the subject.
متن کاملSome Representations for the Generalized Drazin Inverse of Block Matrices in Banach Algebras
We give explicit representations of the generalized Drazin inverse of a block matrix having generalized Schur complement generalized Drazin invertible in Banach algebras. Also we give equivalent conditions under which the group inverse of a block matrix exists and a formula for its computation. The provided results extend earlier works given in the literature. 2010 Mathematics Subject Classific...
متن کاملRepresentation for the generalized Drazin inverse of block matrices in Banach algebras
Several representations of the generalized Drazin inverse of a block matrix with a group invertible generalized Schur complement in Banach algebra are presented.
متن کاملSchur complements and Banachiewicz-Schur forms
Through the matrix rank method, this paper gives necessary and sufficient conditions for a partitioned matrix to have generalized inverses with Banachiewicz-Schur forms. In addition, this paper investigates the idempotency of generalized Schur complements in a partitioned idempotent matrix.
متن کامل