Displaying similar documents to “Extreme preservers of maximal column rank inequalities of matrix sums over semirings”

Zero-term ranks of real matrices and their preservers

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

Czechoslovak Mathematical Journal

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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.

Perimeter preservers of nonnegative integer matrices

Seok-Zun Song, Kyung-Tae Kang, Sucheol Yi (2004)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the perimeter of nonnegative integer matrices. We also characterize the linear operators which preserve the rank and perimeter of nonnegative integer matrices. That is, a linear operator T preserves the rank and perimeter of rank- 1 matrices if and only if it has the form T ( A ) = P ( A ∘ B ) Q , or T ( A ) = P ( A t ∘ B ) Q with appropriate permutation matrices P and Q and positive integer matrix B , where ∘ denotes Hadamard product.

Perimeter preserver of matrices over semifields

Seok-Zun Song, Kyung-Tae Kang, Young Bae Jun (2006)

Czechoslovak Mathematical Journal

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For a rank- 1 matrix A = 𝐚 𝐛 t , we define the perimeter of A as the number of nonzero entries in both 𝐚 and 𝐛 . We characterize the linear operators which preserve the rank and perimeter of rank- 1 matrices over semifields. That is, a linear operator T preserves the rank and perimeter of rank- 1 matrices over semifields if and only if it has the form T ( A ) = U A V , or T ( A ) = U A t V with some invertible matrices U and V.