Perimeter preservers of nonnegative integer matrices

Seok-Zun Song; Kyung-Tae Kang; Sucheol Yi

Displaying similar documents to “Perimeter preservers of nonnegative integer matrices”

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.

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.

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.

Linear maps preserving rank 2 on the space of alternate matrices and their applications.

Cao, Chongguang, Tang, Xiaomin (2004)

International Journal of Mathematics and Mathematical Sciences

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Rank and perimeter preserver of rank-1 matrices over max algebra

Seok-Zun Song, Kyung-Tae Kang (2003)

Discussiones Mathematicae - General Algebra and Applications

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For a rank-1 matrix $A = a \otimes b^{t}$ over max algebra, 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 max algebra. 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) = U ⊗ A ⊗ V, or $T (A) = U \otimes A^{t} \otimes V$ with some monomial matrices U and V.