Permanents of matrices over roots of unity.

Letanddenote the group ofrth roots of unity, the set of allmatrices over, thematrix with all entries 1 and thematrix within the (1, 1)-entry and 1 elsewhere, respectively. Let. Wang proved thatif and only ifAcan be obtained fromby a finite sequence of elementary operations. In this paper, we generalize this result for matrices overby showing that the absolute value of permanent function achieves the maximum value,n!, if and only ifAis the matrix obtained fromby the certain elementary operations. Also, we prove that if, thenand. Among other results we prove that for a complex Hadamard matrix. [ABSTRACT FROM AUTHOR]