The excess of complex Hadamard matrices

Authors

H. Kharaghani
Jennifer Seberry, University of WollongongFollow

Publication Details

H. Kharaghani and Jennifer Seberry, The excess of complex Hadamard matrices, Graphs and Combinatorics, 9, (1993), 47-56.

Abstract

A complex Hadamard matrix, C, of order n has elements 1, -1, i, - i and satisfies CC* = nI_n where C* denotes the conjugate transpose of C. Let C = [c_ij] be a complex Hadamard matrix of order n. S(C) = ∑ c_ij 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.