Daily Archives: April 3, 2015

Solution: 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.)

The best solution was submitted by 엄태현 (수리과학과 2012학번). Congratulations!

Here is his solution of problem 2015-04.

Alternative solutions were submitted by 고경훈 (2015학번, +3), 김경석 (2015학번, +3), 김기현 (수리과학과 2012학번, +3), 박성혁 (수리과학과 2014학번, +3), 오동우 (2015학번, +3), 이명재 (수리과학과 2012학번, +3), 이수철 (수리과학과 2012학번, +3, solution), 이종원 (수리과학과 2014학번, +3, solution), 장기정 (수리과학과 2014학번, +3), 정성진 (수리과학과 2013학번, +3), 진우영 (수리과학과 2012학번, +3), 최인혁 (2015학번, +3).

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