Extreme preservers of maximal column rank inequalities of matrix sums over semirings

Seok-Zun Song; Kwon-Ryong Park

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 $m \times n$ 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 $T (A) = P (A \circ B) Q$ , or $T (A) = P (A^{t} \circ B) Q$ with appropriate permutation matrices $P$ and $Q$ and positive integer matrix $B$ , where $\circ$ 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.