The Moore-Penrose inverse over a commutative ring

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 MR be the category of finite matrices over R with the involution (aij) → (aij)* = (-aij) A matrix A:m → n in MR of determinantal rank r such that u(A) = Σ α ∈ Q r.m Σ α ∈ Q r.m det Aαβ -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 MR, 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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Deposited On:14 Jan 2012 15:25
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