We consider the downlink of a multiuser multiple-input multiple-output (MU-MIMO) system, where each user feeds back a partial channel state information (CSI), namely, the quantized version of the dominant eigenvector of its channel covariance matrix, to the base station (BS) for precoding. Specifically, we propose a downlink multiuser precoding scheme by first reconstructing the equivalent channel matrix of each user via a limited feedback, and then by employing a precoder to suppress the multiuser interference at the receivers. For the single stream case, a signal-to-leakage-and-noise ratio (SLNR) based precoding is employed, while for the full stream case with limited feedback, we employ a lattice reduction aided block diagonalization type precoding with suitable modifications at the receiver side. Extensive numerical examples which are provided using the 5G new radio (5G-NR) channel models demonstrate that the proposed schemes outperform the existing eigenvector based algorithms, and they are more robust against the downlink channel estimation errors.