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A Note on Permutation Equivalence of Boolean Matrices

Let m and n be positive integers and B mn be the set of all m by n Boolean matrices. Let R(A) denote the subspace spanned by the rows of A∈B mn. Denote the cardinality of R(A) by |R(A)|. In this note the author showed that if s is nonnegative integer and A∈B n,n+s, then |R(A)|=2 n if and only if A contains a submatrix which is permutation equivalent to the unit matrix of order n.