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Equivalence of von Neumann regular and idempotent matrices. (English) Zbl 0801.15003
A matrix $$X$$ is a 1-inverse for a matrix $$A$$ if $$AXA = A$$. $$X$$ is a $$\{1,2\}$$-inverse of $$A$$ if in addition $$XAX = X$$. It is shwon that for matrices over certain types of rings that if $$A$$ has a 1-inverse, then it also has a {1,2}-inverse.

MSC:
 15A09 Theory of matrix inversion and generalized inverses
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References:
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