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Rank equalities for block matrices and their Moore-Penrose inverses. (English) Zbl 1057.15006

The author considers: a) the relationship between \(\left[ \begin{smallmatrix} A\\ B \end{smallmatrix} \right] \) and \(\left[ \begin{smallmatrix} A^{† } \\ B^{† } \end{smallmatrix} \right] \), where \(A^{† }\) denotes the Moore-Penrose inverse of \(A\), through some rank equalities, and b) a variety of rank equalities for \( 2\times 2\) block matrices and their Moore-Penrose inverses, that can easily characterize equalities for Moore-Penrose inverses of block matrices.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15A24 Matrix equations and identities
15A03 Vector spaces, linear dependence, rank, lineability
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