Geodesic
Zero-term rank preservers of integer matrices
Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 155-161

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The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.
Keywords: linear operator, term-rank, zero-term rank, (P,Q,B)-operator 
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Song, Seok-Zun; Jun, Young-Bae. Zero-term rank preservers of integer matrices. Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 155-161. http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a1/