Thus, a normalized conference matrix has all 1's in its first row and column, except for a 0 in the top left corner, and is 0 on the diagonal. Let "S" be the matrix that remains when the first row and column of "C" are removed. Then either "n" is evenly even (a multiple of 4), and "S" is antisymmetric (as is the normalized "C" if its first row is negated), or "n" is oddly even (congruent to 2 modulo 4) and "S" is symmetric (as is the normalized "C").