# Article

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Keywords:
linear operator; rank; perimeter; \$(P, Q, B)\$-operator
Summary:
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.
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