Complex Hadamard Matrix

A complex Hadamard matrix of order is an matrix whose entries have absolute value one and satisfy . Here is the conjugate transpose. Dividing its columns by gives an orthonormal basis unbiased to the coordinate basis. A complex Hadamard matrix with real entries is a Hadamard matrix with entries 1 and . The discrete Fourier matrix is an example. Equivalence permits row and column permutations and multiplication of individual rows or columns by complex numbers of absolute value one.