# 问题：

Suppose $V$ is a vector space with basis vectors $|0\rangle$ and $|1\rangle$,and $A$ is a linear operator from $V$ to $V$ such that $A|0\rangle=|1\rangle$ and $A|1\rangle=|0\rangle$. Give a matrix representation for $A$,with respect to the input basis $|0\rangle,|1\rangle$ , and the output basis$|0\rangle,|1\rangle$. Find input and output bases which give rise to a different matrix representation of $A$.

## 解答：

A|0\rangle=0|0\rangle+1|1\rangle \\A|1\rangle=1|0\rangle+0|1\rangle
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#### 参考

[1]www.qtumist.com