# 问题：

Find the eigenvectors, eigenvalues, and diagonal representations of the Pauli matrices$X$, $Y$ and $Z$.

## 解答

$X$=$\left(\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right)$,建立方程$\left|\begin{array}{cc} 0-\lambda & 1 \\ 1 & 0-\lambda \end{array}\right|=0$，

$Y$=$\left(\begin{array}{ll} 0 & -i \\ i & 0 \end{array}\right)$,建立方程$\left|\begin{array}{cc} 0-\lambda & -i \\ i & 0-\lambda \end{array}\right|=0$，

$Z$=$\left(\begin{array}{ll} 1 & 0 \\ 0 & -1 \end{array}\right)$,建立方程$\left|\begin{array}{cc} 1-\lambda & 0 \\ 0 & -1-\lambda \end{array}\right|=0$，

#### 参考

[1]www.qtumist.com