Complex Hadamard matrices from Sylvester inverse orthogonal matrices

摘要

A novel method to obtain parametrizations of complex inverse orthogonalmatrices is provided. These matrices are natural generalizations of complexHadamard matrices which depend on non zero complex parameters. The method weuse is via doubling the size of inverse complex conference matrices. When thefree parameters take values on the unit circle the inverse orthogonal matricestransform into complex Hadamard matrices, and in this way we find newparametrizations of Hadamard matrices for dimensions n= 8,10,12.