# 问题：

Repeat the proof of the spectral decomposition in Box 2.2 for the case when M is Hermitian, simplifying the proof wherever possible.

## 解答

Hermitian算子的对角化：方法与过程是相似的，可以简化的理由是算子$M$的自伴随性质，故$QMQ$的正规性立即可得.

$$M = (P + Q)M(P + Q) = PMP + QMP + PMQ + QMQ.$$

$$PMP = λP，QMP =PMQ= 0,$$

$$(QMQ)^{\dagger}=QMQ.$$

#### 参考

[1]www.qtumist.com