# 问题：

Show that all eigenvalues of a unitary matrix have modulus 1, that is, can be written in the form $e^{iθ}$ for some real $θ$.

## 解答

$$U\left|v\right\rangle=\lambda\left|v\right\rangle，$$

$$\left|v\right\rangle^{\dagger} U^{\dagger}=\lambda^{\dagger} \left|v\right\rangle^{\dagger} ，$$

$$\left|v\right\rangle^{\dagger} U^{\dagger} U \left|v\right\rangle=\lambda^{\dagger} \left|v\right\rangle^{\dagger} \lambda \left|v\right\rangle ，$$

#### 参考

[1]www.qtumist.com