Abstract
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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 Springer-Verlag.