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Group inverse for the block matrices with an invertible subblock. (English) Zbl 1181.15003

Suppose that \(M = \left(\begin{matrix} A & B \\ C & D \end{matrix} \right)\) (\(A\) is square) is a square block matrix with an invertible subblock over a skew field \(K\). The authors presented some necessary and sufficient conditions for the existence as well as the expressions of the group inverse for \(M\) under some conditions.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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