In this paper, we study deterministic linear precoding and combining for a single-user multiple-input multiple-output communication system in flat Rayleigh fading. We consider differential encoding at the transmitter and differential detection using a maximum likelihood decision rule at the receiver. The precoding matrix is designed to maximize the bound on the average received signal-to-noise ratio, whereas the combining matrix is structured to minimize the union bound on the symbol error probability (SEP). In addition, we present a comprehensive evaluation of the error performance in terms of the pairwise error probability and the SEP.