Geodesic
Perimeter preservers of nonnegative integer matrices
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 1, pp. 9-15
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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.
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.
Classification : 15A04, 15A30, 15A33, 15A36, 15A48
Keywords: linear operator; rank; perimeter; $(P, Q, B)$-operator 
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     title = {Perimeter preservers of nonnegative integer matrices},
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     year = {2004},
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Song, Seok-Zun; Kang, Kyung-Tae; Yi, Sucheol. Perimeter preservers of nonnegative integer matrices. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 1, pp. 9-15. http://geodesic.mathdoc.fr/item/CMUC_2004_45_1_a1/