Geodesic
Zero-term ranks of real matrices and their preservers
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 183-188.

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Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve zero-term rank of the $m \times n$ real matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix.
Classification : 15A03, 15A04
Keywords: linear operator; zero-term rank; $P, Q, B$-operator 
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     title = {Zero-term ranks of real matrices and their preservers},
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Beasley, LeRoy B.; Jun, Young-Bae; Song, Seok-Zun. Zero-term ranks of real matrices and their preservers. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 183-188. http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a15/