Counting Matrices with Coordinates in Finite Fields and of Fixed Rank.

Dan Laksov; Anders Thorup

Displaying similar documents to “Counting Matrices with Coordinates in Finite Fields and of Fixed Rank.”

Preservers of the rank of matrices over a field.

Kalinowski, Józef (2009)

Beiträge zur Algebra und Geometrie

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Zero-term rank preservers of integer matrices

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

Discussiones Mathematicae - General Algebra and Applications

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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.