[math] \newcommand{\mathds}{\mathbb}[/math]

If [math]H\in M_M(\mathbb T)[/math] and [math]K\in M_N(\mathbb T)[/math] are complex Hadamard matrices, prove that so is the matrix

[[math]] H\otimes_QK\in M_{MN}(\mathbb T) [[/math]]

given by the following formula, with [math]Q\in M_{M\times N}(\mathbb T)[/math],

[[math]] (H\otimes_QK)_{ia,jb}=Q_{ib}H_{ij}K_{ab} [[/math]]

called Di\c t\u a deformation of [math]H\otimes K[/math], with parameter [math]Q[/math].