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McDonald, Judith J., Olesky, D.Dale, Schneider, Hans, Tsatsomeros, Michael J., van den Driessche, P. (1998)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Zero-one completely positive matrices and the A(R, S) classes

G. Dahl, T. A. Haufmann (2016)

Special Matrices

A matrix of the form A = BBT where B is nonnegative is called completely positive (CP). Berman and Xu (2005) investigated a subclass of CP-matrices, called f0, 1g-completely positive matrices. We introduce a related concept and show connections between the two notions. An important relation to the so-called cut cone is established. Some results are shown for f0, 1g-completely positive matrices with given graphs, and for {0,1}-completely positive matrices constructed from the classes of (0, 1)-matrices...

Zero-term rank preservers of integer matrices

Seok-Zun Song, Young-Bae Jun (2006)

Discussiones Mathematicae - General Algebra and Applications

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.

Zero-term ranks of real matrices and their preservers

LeRoy B. Beasley, Young Bae Jun, Seok-Zun Song (2004)

Czechoslovak Mathematical Journal

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 × n real matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix.

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