A complex Hadamard matrix is any complex N × N {\displaystyle N\times N} matrix H {\displaystyle H} satisfying two conditions: unimodularity : | H j k | = 1 f o r j, k = 1, 2, …, N {\displaystyle |H_{jk}|=1{\quad {\rm {for\quad }}}j,k=1,2,\dots,N} orthogonality: H H † = N I {\displaystyle HH^{\dagger }=NI},where † {\displaystyle {\dagger }} denotes the Hermitian transpose of H {\displaystyle H} and I {\displaystyle I} is the identity matrix. Wikipedia