Low-rank matrix factorization has been exploited in a variety of contexts to improve the optimization
problems. Given an m×n matrix C of rank r, there exists a factorization C = AB where A is an m×r full
column rank matrix and B is an r×n full row rank matrix. Thus, we can replace C by A and B. To reduce
the parameters of C by a fraction p, it is essential to ensure that mr+rn < pmn, i.e., the rank of C should
satisfy that r < pmn/(m + n).