In many network communication scenarios, a relay in the network may only need to recover and retransmit an equation of the transmitted messages. In previous work, it has been shown that if each transmitter employs the same lattice code, the interference structure of the channel can be exploited to recover an equation much more efficiently than possible with standard multiple-access strategies. Here, we generalize this compute-and-forward framework to the multiple antenna setting. Our results show that it is often beneficial to use extra antennas at the receiver to rotate the channel coefficients towards the nearest integer vector instead of separating out the transmitted signals. We also demonstrate that in contrast to classical strategies, the multiplexing gain of compute-and-forward increases if the transmitters have channel state information. Finally, we apply our scheme to the two way relay network and observe performance gains over traditional strategies.