# 基本现代操作np.linalg

## **norm实现数据归一化**

```python
import numpy as np
x=np.array([[0, 3, 4], [2, 6, 4]])
y=np.linalg.norm(x, axis=1, keepdims=True)
z=x/y
```

![img](/files/-LpsmaDEaEcEn0EJFXa9)

* ord ： 为设置具体范数值， axis 向量的计算方向。
* axis=1表示按行向量处理，求多个行向量的范数
* axis=0表示按列向量处理，求多个列向量的范数
* keepdims：是否保持矩阵的二维特性，True表示保持矩阵的二维特性，False相反

## 范数

```python
x = np.array([
    [0, 3, 4],
    [1, 6, 4]])
#默认参数ord=None，axis=None，keepdims=False
print "默认参数(矩阵整体元素平方和开根号，不保留矩阵二维特性)：",np.linalg.norm(x)
print "矩阵整体元素平方和开根号，保留矩阵二维特性：",np.linalg.norm(x,keepdims=True)

print "矩阵每个行向量求向量的2范数：",np.linalg.norm(x,axis=1,keepdims=True)
print "矩阵每个列向量求向量的2范数：",np.linalg.norm(x,axis=0,keepdims=True)

print "矩阵1范数：",np.linalg.norm(x,ord=1,keepdims=True)
print "矩阵2范数：",np.linalg.norm(x,ord=2,keepdims=True)
print "矩阵∞范数：",np.linalg.norm(x,ord=np.inf,keepdims=True)

print "矩阵每个行向量求向量的1范数：",np.linalg.norm(x,ord=1,axis=1,keepdims=True)
```

## 高阶

**线性模型系数估计**：a=np.linalg.lstsq(x,b),有b=a\*x

求方阵的**逆矩阵**np.linalg.inv(A)

求**广义逆矩阵**：np.linalg.pinv(A)

求矩阵的**行列式**：np.linalg.det(A)

**解形如AX=b的线性方程组**：np.linalg.solve(A,b)

求矩阵的**特征值**：np.linalg.eigvals（A）

求特征值和**特征向量**：np.linalg.eig(A)

**Svd分解**：np.linalg.svd(A)


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