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[eig_circulant] Update translations #46

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14 changes: 5 additions & 9 deletions lectures/eig_circulant.md
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Original file line number Diff line number Diff line change
Expand Up @@ -83,7 +83,7 @@ def construct_cirlulant(row):
```

```{code-cell} ipython3
# 一个简单的例子，当 N = 3 时
# 当 N = 3 时的一个简单例子
construct_cirlulant(np.array([1., 2., 3.]))
```

Expand Down Expand Up @@ -317,7 +317,7 @@ Q8 = F8 / np.sqrt(8)
```

```{code-cell} ipython3
# 验证正交性（酉性）
# 验证正交性
Q8 @ np.conjugate(Q8)
```

Expand All @@ -338,20 +338,16 @@ for j in range(8):
diff_arr
```

## 关联置换矩阵
## 循环矩阵与置换矩阵的关系

接下来，我们执行计算来验证方程 {eq}`eqn:circulant` 中定义的循环矩阵 $C$ 可以写成
接下来，我们将验证方程 {eq}`eqn:circulant` 中定义的循环矩阵 $C$ 可以表示为置换矩阵的线性组合：

$$
C = c_{0} I + c_{1} P + \cdots + c_{n-1} P^{n-1}
$$

并且 $P$ 的每个特征向量也是 $C$ 的特征向量。

```{code-cell} ipython3

```

我们用 $N=8$ 的情况来说明这一点。

```{code-cell} ipython3
Expand All @@ -366,7 +362,7 @@ c
C8 = construct_cirlulant(c)
```

计算 $c_{0} I + c_{1} P + \cdots + c_{n-1} P^{n-1}$。
计算 $c_{0} I + c_{1} P + \cdots + c_{n-1} P^{n-1}$

```{code-cell} ipython3
N = 8
Expand Down
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