Tensor notations in multivariate mixed model

Hi everyone,
I have the attached multivariate mixed model in matrix notations. I have been advised to use tensor notations to simplify the model formulation in the multivariate case. Since, I am unfamiliar with the tensor notations, I looked at different online resources but I get lost very quickly and I have no idea where to start. Could someone help/guide me with this or indicate any resource that could be helpful?
Thanks in advance