The maximal and minimal ranks of A − BXC with applications
Yongge Tian, Cheng Shi-zhen · 2003
We consider how to take X such that the linear matrix expression A−BXC attains its maximal and minimal ranks, respectively. As applications, we investigate the rank invariance and the range invariance of A − BXC with respect to the choice of X. In addition, we also give the general solution of the rank equation rank(A − BXC) + rank(BXC) = rank(A) and then determine the minimal rank of A − BXC subject to this equation. 345 2. The maximal and minimal ranks of A − BXC with respect to X 349 3. Solutions to the equation rank(A − BXC) + rank(BXC) = rank(A) 357 4. Summary