In this paper, for spatial multiplexing with limited feedback, we propose quantized principal component selection (QPCS) precoding, wherein the active bases are selected at the receiver from a finite number of basis sets known at the both receiving and transmitting ends, conveyed to the transmitter using limited feedback, and assembled into a precoding matrix at the transmitter. The selected bases are conveyed to the transmitter using feedback information on both the index of the selected basis set, which defines the most appropriate set of coordinates for describing a multiple-input multiple-output (MIMO) channel, and the principal bases with the largest gain in the selected basis set. A systematic design method for a finite number of basis sets using the antenna array processing is presented. We show that the proposed QPCS precoding scheme provides comparable capacity with the closed-loop MIMO with full channel state information (CSI), even with limited feedback. Furthermore, for practical implementation of the QPCS precoding scheme, we propose a low complex structured precoder optimization procedure and show that the proposed procedure induces a negligible capacity loss compared with the exhaustive precoder optimization, even with considerably reduced complexity.