In this letter, we consider time-varying complex-valued n × m matrices H[k] (m ≤ n) and propose a predictive quantizer for the eigenvectors of the Gramian H[k]H[k]^H, which operates on the associated compact Stiefel manifold. The proposed quantizer exploits the temporal correlation of the source signal to provide high-fidelity representations with significantly reduced quantization codebook size compared to memoryless schemes. We apply the quantizer to channel state information quantization for limited feedback based multi-user MIMO, employing regularized block-diagonalization precoding. We demonstrate significant rate gains compared to block-diagonalization precoding using Grassmannian predictive feedback.