2009•Bulletin of Science and TechnologyRequires access

The Г_(αβ)-Moore-Penrose Inverse of Matrices over Rings

Cen Jian-miao

Abstract

The Гαβ-generalized inverse and Гαβ-Moore-Penrose inverse of matrices over a ring are discussed.The necessary and sufficient conditions for existence and the explicit expressions of the Гαβ-generalized inverse and Гαβ-Moore-Penrose inverse of a kind of decomposable matrices over a ring with an involution * and unitary are given,and some pre-vious results are extended.

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Key concepts: Inverse, Involution (esoterism), Mathematics, Moore–Penrose pseudoinverse, Generalized inverse, Unitary state, Pure mathematics, Inverse function