# 2015-4 An inequality on positive semidefinite matrices

Let $$M=\begin{pmatrix} A & B \\ B^*& C \end{pmatrix}$$ be a positive semidefinite Hermian matrix. Prove that $\operatorname{rank} M \le \operatorname{rank} A +\operatorname{rank} C.$ (Here, $$A$$, $$B$$, $$C$$ are matrices.)

GD Star Rating