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On reverse-order laws for least-squares g-inverses and minimum norm g-inverses of a matrix product. (English) Zbl 1125.15006

The reverse order law is analyzed for some kinds of generalized inverses: \((1,3)\) and \((1,4)\) generalized inverses and the Moore-Penrose inverse. For example, relations indicating when \(B^{(1,i)}A^{(1,i)} \in (AB)^{(1,i)}\) are studied for \(i=3,4\) and when the equality holds for the Moore-Penrose inverse.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15A03 Vector spaces, linear dependence, rank, lineability
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