You have M antennas at the transmitting side & N antennas at the receiving side. The i-th transmitting antenna sends an EM wave  x_i  and the receiving party obtains y_j on its j-th antenna. Since the EM wave carrying the signal has two degrees of freedom, we can view this as a map 𝑥∈ℂᴹ→𝑦∈ℂᴺ.

2/n