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Reflexive generalized inverses and their minors. (English) Zbl 0787.15006
Suppose that $$A$$ is an $$m\times n$$ matrix. Then $$G$$ is a reflexive $$g$$- inverse of $$A$$ if $$AGA=A$$ and $$G=GAG$$. The matrices $$A$$, $$G$$ are taken to be over either the real numbers or an integral domain. All reflexive $$g$$- inverses of a matrix $$A$$ of rank $$r$$ are characterized. A general form for reflexive $$g$$-inverses of $$A$$ is given in terms of the minors of the $$r\times r$$ submatrices of $$A$$. The minors of reflexive $$g$$-inverses of $$A$$ are also given in terms of the minors of $$A$$.

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