In this paper, we study self energy recycling techniques for point-to-point multiple-input multiple-output systems where a full-duplex transmitter with multiple antennas communicates with a multi-antenna receiver. Due to the full-duplex nature, the transmitter receives a signal transmitted by itself through a loop-back channel. Then, the energy of the signal is harvested and stored in an energy storage. Assuming timeslotted systems, we propose a new communication protocol in which the harvested energy at the transmitter is recycled for future data transmissions to the receiver. Under this setup, we present a transmit covariance matrix optimization method in order to maximize the sum rate performance for two different cases. First, for a perfect channel state information (CSI) case, the globally optimal algorithm for the sum rate maximization problem is proposed. Next, for an imperfect CSI case, we provide a robust covariance matrix optimization approach where the worst-case sum rate performance can be maximized. Numerical results demonstrate that the proposed methods offer a significant performance gain over conventional schemes.