Block representations of the Drazin inverse of a bipartite matrix.

Catral, Minerva; Olesky, Dale D.; van den Driessche, Pauline

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A new rank formula for idempotent matrices with applications

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Commentationes Mathematicae Universitatis Carolinae

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It is shown that $rank (P^{*} A Q) = rank (P^{*} A) + rank (A Q) - rank (A),$ where $A$ is idempotent, $[P, Q]$ has full row rank and $P^{*} Q = 0$ . Some applications of the rank formula to generalized inverses of matrices are also presented.

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