NOTE 1 For a unitary matrix with elements A_ij:

${\displaystyle \sum _i{A}_{ij}{A}_{ik}^{*}}={\delta }_{jk}$ and ${\displaystyle \sum _k{A}_{ik}{A}_{jk}^{*}}={\delta }_{ij}$

where ${\delta }_{jk}$ and ${\delta }_{ij}$ are Kronecker deltas.

NOTE 2 Any orthogonal matrix with real elements is a unitary matrix.