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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-one matrices with an application to abelian groups

Ulrich F. Albrecht, H. Pat Goeters, Charles Megibben (1993)

Rendiconti del Seminario Matematico della Università di Padova

Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains.

Eiermann, Michael, Varga, Richard S. (1993)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Zeros of unilateral quaternionic polynomials.

De Leo, Stefano, Ducati, Gisele, Leonardi, Vinicius (2006)

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

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 $m \times n$ real matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix.