Zero-term rank preservers of integer matrices

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.

Preservers of the rank of matrices over a field.

Kalinowski, Józef (2009)

Beiträge zur Algebra und Geometrie

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A note on quasiconvexity and rank-one convexity for $2 \times 2$ matrices.

Pedregal, Pablo, Šverák, Vladimír (1998)

Journal of Convex Analysis

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