1.标量, 向量, 矩阵, 张量
import numpy as np
s = 5
V = np.array([1,2])
m = np.array([[1,2],[2,4]])
t = np.array([
[[1,2,3],[4,5,6],[7,8,9]],
[[11,12,13],[14,15,16],[17,18,19]],
[[21,22,23],[24,25,26],[27,28,29]],
])
print("标量:\n" + str(s))
print("向量:\n" + str(V))
print("矩阵:\n" + str(m))
print("张量:\n" + str(t))
2.矩阵转置
A = np.array([[1.0,2.0],[1.0,1.0],[2.0,3.0]])
A_t = A.transpose()
print("A:\n",A)
print("A_t:\n",A_t)
3.矩阵加法
a = np.array([[1.0,2.0],[3.0,4.0]])
b = np.array([[6.0,7.0],[8.0,9.0]])
print("矩阵相加:\n",a+b)
4.矩阵乘法
m1 = np.array([[1.0,3.0],[1.0,0.0]])
m2 = np.array([[1.0,2.0],[5.0,0.0]])
print("按矩阵乘法规则:\n",np.dot(m1,m2))
print("按逐元素相乘:\n",np.multiply(m1,m2))
print("按逐元素相乘:\n",m1*m2)
v1 = np.array([1.0,2.0])
v2 = np.array([4.0,5.0])
print("向量内积:\n",np.dot(v1,v2))
5.单位矩阵
print("单位矩阵")
np.identity(3)
6.矩阵的逆
A = [[1.0,2.0],[3.0,4.0]]
A_inv = np.linalg.inv(A)
print("A的逆矩阵:\n",A_inv)
7.范数
a = np.array([[1.0,3.0]])
print("向量 2 范数:\n",np.linalg.norm(a,ord = 2))
print("向量 1 范数:\n",np.linalg.norm(a,ord = 1))
print("向量无穷范数:\n",np.linalg.norm(a,ord = np.inf))
a = np.array([[1.0,3.0],[2.0,1.0]])
print("矩阵 F 范数:\n",np.linalg.norm(a,ord = "fro"))
8.特征值分解
A = np.array([[1.0,2.0,3.0],
[4.0,5.0,6.0],
[7.0,8.0,9.0]])
print("特征值:\n",np.linalg.eigvals(A))
eigvals, eigvectors = np.linalg.eig(A)
print("特征值:\n",eigvals)
print("特征向量:\n",eigvectors)
9.奇异值分解
A = np.array([[1.0,2.0,3.0],
[4.0,5.0,6.0]])
U, D, V = np.linalg.svd(A)
print("U:\n",U)
print("D:\n",D)
print("V:\n",V)