Complex Hadamard matrix (original) (raw)

A complex Hadamard matrix is any complex matrix satisfying two conditions: * unimodularity (the modulus of each entry is unity): * orthogonality: , where denotes the Hermitian transpose of and is the identity matrix. The concept is a generalization of the Hadamard matrix. Note that any complex Hadamard matrix can be made into a unitary matrix by multiplying it by ; conversely, any unitary matrix whose entries all have modulus becomes a complex Hadamard upon multiplication by . belong to this class.