Displaying similar documents to “Linear maps preserving rank 2 on the space of alternate matrices and their applications.”

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.

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.

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that rank ( P * A Q ) = rank ( P * A ) + rank ( A Q ) - rank ( A ) , where A is idempotent, [ P , Q ] has full row rank and P * Q = 0 . Some applications of the rank formula to generalized inverses of matrices are also presented.

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.