Can anybody tell me whether it is possible to have a set of 4 complex $N\times N$ matrices:
$$A^\mu A^\nu + A^{T\mu}A^{T\nu} = \eta^{\mu\nu}I$$
Where $A^{T\mu}$ is the transpose of $A^\mu$, $I$ is the $N\times N$ identity matrix and $\eta^{\mu\nu}=diag(1,-1,-1,-1)$ is the Minkowski Metric.