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A wireless relay with multiple antennas is called a multiple-input-multiple-output (MIMO) switch if it maps its input links to its output links using "precode-and-forward." Namely, the MIMO switch precodes the received signal vector in the uplink using some matrix for transmission in the downlink. This paper studies the scenario of K stations and a MIMO switch, which has full channel state information. The precoder at the MIMO switch is either a zero-forcing matrix or a network-coding matrix. With the zero-forcing precoder, each destination station receives only its desired signal with enhanced noise but no interference. With the network-coding precoder, each station receives not only its desired signal and noise, but possibly also self-interference, which can be canceled. Precoder design for optimizing the received signal-to-noise ratios at the destinations is investigated. For zero-forcing relaying, the problem is solved in closed form in the two-user case, whereas in the case of more users, efficient algorithms are proposed and shown to be close to what can be achieved by extensive random search. For network-coded relaying, we present efficient iterative algorithms that can boost the throughput further.