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. Disciplines Physical Sciences and Mathematics Publication Details H. Kharaghani and Jennifer Seberry, The excess of complex Hadamard matrices, Graphs and Combinatorics, 9, (1993), 47-56. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1072 Graphs and Combinatorics (1993) 9: 47-56 Graphs and Combinatorics © Springer-Verlag 1993 The Excess of Complex Hadamard Matrices H. KharaghanP* and Jennifer Seberry2** 1 Department of Mathematical Sciences, The University of Lethbridge, Lethbridge, Alberta, TlK 3M4, Canada 2 Department of Computer Science, University ofWollongong, Wollongong, NSW 2500, Australia Abstract. A complex Hadamard matrix, C, of order n has elements 1, -1, i, i and satisfies CC* = nI. where C* denotes the conjugate transpose of C. Let C = [cijJ be a complex Hadamard matrix of order n. S(C) = I Cij is called the sum of C. u(C) = IS(c)1 is called the excess of C. We ij study the excess of complex Hadamard matrices. As an application many real Hadamard matrices of large and maximal excess are obtained. A complex Hadamard matrix, C, of order n has elements 1, -1, i, i and satisfies CC* = nI. where C* denotes the conjugate transpose of C. Let C = [cijJ be a complex Hadamard matrix of order n. S(C) = I Cij is called the sum of C. u(C) = IS(c)1 is called the excess of C. We ij study the excess of complex Hadamard matrices. As an application many real Hadamard matrices of large and maximal excess are obtained.