Hadamard matrix
Regular Hadamard matrices are real Hadamard matrices whose row and column sums are all equal. A necessary condition on the existence of a regular "n"×"n" Hadamard matrix is that "n" be a perfect square. A circulant matrix is manifestly regular, and therefore a circulant Hadamard matrix would have to be of perfect square order. Moreover, if an "n"×"n" circulant Hadamard