The excess of complex Hadamard matrices

A complex Hadamard matrix, C, of order n has elements 1, -1, i, - i and satisfies CC* = nIn where C* denotes the conjugate transpose of C. Let C = [cij] be a complex Hadamard matrix of order n. S(C) = ∑ cij is called the sum of C. 0(C) = │S(C)│ is called the excess of C. We study the excess of complex Hadamard matrices. As an application many real Hadamard matrices of large and maximal excess are obtained.