The excess of complex Hadamard matrices

AbstractA complex Hadamard matrix,C, of ordern has elements 1, −1,i, −i and satisfiesCC*=nInwhereC* denotes the conjugate transpose ofC. LetC=[cij] be a complex Hadamard matrix of order $$n. S(C) = \sum\limits_{ij} {c_{ij} } $$ is called the sum ofC. σ(C)=|S(C)| is called the excess ofC. We study the excess of complex Hadamard matrices. As an application many real Hadamard matrices of large and maximal excess are obtained.

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