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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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