Before revision:  We provide theoretical justification for the proposed BELT method . Simulation studies show that the method performs well in finite sample under a variety of configurations.
After revision:  Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices using their overlap, then complete the missing blocks by the inner product of the two low-rank components. Besides, we prove the statistical rate for the eigenspace of the underlying matrix, which is comparable to the rate under the independently missing assumption . Simulation studies show that the method performs well in finite sample under a variety of configurations.