Bapat, R. B. ; Robinson, Donald W.
(1992)
*The Moore-Penrose inverse over a commutative ring*
Linear Algebra and its Applications, 177
.
pp. 89-103.
ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0024-3795(92)90318-5

## Abstract

Let R be a commutative ring with 1 and with an involution a → ā, and let M_{R} be the category of finite matrices over R with the involution (a_{ij}) → (a_{ij})* = (^{-}a_{ij}) A matrix A:m → n in M_{R} of determinantal rank r such that u(A) = Σ _{α ∈ Q r.m} Σ _{α ∈ Q r.m} det A_{αβ} -det^{-}-Ā-_{αβ} has a Moore-Penrose inverse u(A)^{†} in R is said to be Moore invertible with Moore idempotent u(A)u(A)^{†} if u(A)u(A)†A = A. For every matrix A of M_{R}, A has a Moore-Penrose inverse with respect to ∗ if and only if A is the sum of Moore invertible matrices whose Moore idempotents are pairwise orthogonal.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 77806 |

Deposited On: | 14 Jan 2012 15:25 |

Last Modified: | 14 Jan 2012 15:25 |

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