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.)

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  1. Pingback: Problem Solving (KAIST Math Problem of the Week 2015-4) | Math Made in Heaven

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