We consider the design of a multi-input multi-output (MIMO) transmission system equipped with distributed, single-antenna amplify-and-forward relays. In particular, we consider how to optimize the complex forwarding coefficients of the relays to maximize the system capacity. Existing studies on MIMO relay network designs mostly concentrate on the case of single relay with multiple antennas, whose results are not applicable to distributed networks. We first analyze how the system capacity relates to the relay transmission powers and the channel coefficients. An upper bound on the asymptotic capacity at high relay powers is derived. Aided by the capacity results, we consider the optimization of relay coefficients under two noise conditions: that where the destination noise dominates the total noise and that where the relay noise dominates the total noise. It turns out that no simple analytic solutions can be found for all relay network sizes. Therefore, we propose suboptimal solutions that involve computation of optimal relay coefficients with optimal selection of relays for network sizes that can be solved analytically. The results on diversity order are found to show resemblance to that for single-hop MIMO systems employing antenna selection. Simulation results also verify the superior performance of the proposed technique.