## 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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### References:

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