Complex Hadamard matrices from Sylvester inverse orthogonal matrices

Details Complex Hadamard matrices from Sylvester inverse orthogonal matrices Complex Hadamard matrices from Sylvester inverse orthogonal matrices

2009-01-08

arxiv.org/abs/0901.0982v3

Physics

Mathematical Physics

revised form of the paper published in Open Systems & Information Dynamics, 16 (2009) 387-405

Scientific paper

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

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