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Reconfigurable intelligent surface (RIS) technology has recently gained a lot of attention since it promises to enhance the spectral and energy efficiency of future wireless communication systems. In this paper, we propose several approaches to optimize the beamformers at the base station (BS) and the phase shifts at the RIS for an RIS-assisted multiple-input multiple-output (MIMO) system. By comparing the minimum signal power, minimum signal to interference plus noise ratio (SINR) and rate achieved by the proposed maximum ratio transmission (MRT), zero-forcing (ZF) and max min SINR based optimizations, we conclude that the MRT based optimization can achieve the highest minimum signal power among other approaches, whereas the max min SINR optimization can achieve the highest minimum SINR and minimum rate. In addition, the effect of quantized RIS-phase shifts is analyzed, showing that almost …