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Keywords:
linear operator; zero-term rank; $P,Q,B$-operator
linear operator; zero-term rank; $P,Q,B$-operator
Summary:
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.
References:
[1] L. B. Beasley and N. J. Pullman: Term-rank, permanent and rook-polynomial preservers. Linear Algebra Appl. 90 (1987), 33–46. DOI 10.1016/0024-3795(87)90302-8 | MR 0884107
[2] L. B. Beasley, S. Z. Song and S. G. Lee: Zero-term rank preservers. Linear and Multilinear Algebra 48 (2001), 313–318. DOI 10.1080/03081080108818677 | MR 1928400
[3] C. R. Johnson and J. S. Maybee: Vanishing minor conditions for inverse zero patterns. Linear Algebra Appl. 178 (1993), 1–15. MR 1197498
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