# 问题：

Suppose $|v_{i}\rangle$ is an orthonormal basis for an inner product space $V$. What is the matrix representation for the operator $|v_{j}\rangle\langle v_{k}|$, with respect to the $|v_{i}\rangle$ basis?

## 解答

$$A=I_{W} A I_{V}=\sum_{i j}\left|w_{j}\right\rangle\left\langle w_{j}|A| v_{i}\right\rangle\left\langle v_{i}\right|=\sum_{i j}\left\langle w_{j}|A| v_{i}\right\rangle\left|w_{j}\right\rangle\left\langle v_{i}\right|.$$

#### 参考

[1]www.qtumist.com