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This paper studies large multiple-input multiple-output (MIMO) communication systems with linear precoding and reduced-rank Krylov subspace receivers. We design precoders and analyze their performance by exploiting large-dimensional random matrix theory. We first devise low-complexity precoding schemes that can improve performance of low-rank Krylov subspace receivers in the regime of high signal-to-noise ratio (SNR). We then introduce a potential theory-based method for analyzing the convergence behavior of the mean-squared error (MSE) for various transmission schemes. This method can be applied to a broader range of problems compared to previous analytical tools. The analysis reveals that the MSE decreases super exponentially with the rank of the receiver. Numerical examples show that the proposed precoders can outperform conventional precoders when low-rank Krylov subspace receivers are used, and that the performance of such receivers can be accurately predicted.