Complex Hadamard matrix

Complex Hadamard matrices

A complex Hadamard matrix is any complex N×N matrix H satisfying two conditions:

      $|H_{jk}|=1{\quad {\rm {for\quad }}}j,k=1,2,\dots ,N$

$HH^{\dagger }=N{\mathbb {1} }$

where  

$^{\dagger }$ denotes the hermitian transpose of H and ${\mathbb {1} }$ is the identity matrix