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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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