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This paper addresses joint transceiver and relay design for a wireless multiple-input multiple-output (MIMO) switching scheme that enables data exchange among multiple users. Here, a multiantenna relay linearly precodes the received (uplink) signals from multiple users and forwards the signal in the downlink, where the purpose of precoding is to let each user receive its desired signal with interference from other users suppressed. The problem of optimizing the precoder based on various design criteria is typically nonconvex and difficult to solve. The main contribution of this paper is a unified approach to solve the weighted sum mean square error (MSE) minimization and weighted sum rate maximization problems in MIMO switching. Specifically, an iterative algorithm is proposed for jointly optimizing the relay's precoder and the users' receive filters to minimize the weighted sum MSE. It is also shown that the weighted sum rate maximization problem can be reformulated as an iterated weighted sum MSE minimization problem and can, therefore, be solved similarly to the case of weighted sum MSE minimization. With properly chosen initial values, the proposed iterative algorithms are asymptotically optimal in both high- and low-signal-to-noise-ratio regimes for MIMO switching, either with or without self-interference cancellation (a.k.a., physical-layer network coding). Numerical results show that the optimized MIMO switching scheme based on the proposed algorithms significantly outperforms existing approaches in the literature.