Abstract

A complex Hadamard matrix, C, of order n has elements 1, 1, i, i and satisfies CC*=nInwhere C* denotes the conjugate transpose of C. Let C=[cij] be a complex Hadamard matrix of order {Mathematical expression} is called the sum of C. σ(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. © 1993 SpringerVerlag.