NumPy之矩阵向量线性代数等操作示例

[1 2 3]
[4 5 6]

import numpy as np
v = np.array([1, 2, 3, 4, 5])

import numpy as np
# 创建一维数组
v = np.array([1, 2, 3])
print(v)  # 输出：[1 2 3]

import numpy as np
# 创建二维数组
m = np.array([[1, 2, 3], [4, 5, 6]])
print(m)  # 输出：[[1 2 3]
          #      [4 5 6]]

import numpy as np
# 创建一维数组
v = np.array([1, 2, 3])
# 访问元素
print(v[0])  # 输出：1
print(v[1])  # 输出：2
print(v[2])  # 输出：3

import numpy as np
# 创建矩阵
A = np.array([[1, 2], [3, 4]])
# 转置矩阵
AT = np.transpose(A)
print(AT)  # 输出：[[1 3]
           #      [2 4]]
print (A.T)    

# 矩阵加法
np.add(A, B)
# 矩阵减法
np.subtract(A, B)
# 矩阵乘法
# 在进行矩阵乘法时，前一个矩阵的列数必须等于后一个矩阵的行数，才能进行乘法运算
# (M行, N列)*(N行, L列) = (M行, L列)
p.dot(A, B)
# 矩阵除法
np.divide(A, B)

import numpy as np
# 创建矩阵A和B
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
print("A + B:")
print(np.add(A, B))
[1, 2]  	[5, 6]		[6, 8]
		+  			=  
[3, 4]		[7, 8]		[10, 12]
print("A - B:")
print(np.subtract(A, B))
[1, 2]  	[5, 6]		[-4, -4]
		-  			=  
[3, 4]		[7, 8]		[-4, -4]
print("A * B:")
print(np.dot(A, B))
[1, 2]  	[5, 6]		[19, 22]
		*  			=  
[3, 4]		[7, 8]		 [43, 50]
print("A / B:")
print(np.divide(A, B))
[1, 2]  	[5, 6]		[0.2,  0.33333333]
		/  			=  
[3, 4]		[7, 8]		[0.42857143, 0.5]

[1, 2]  	[1]			[19]
		*  			=  
[3, 4]		[1]			 [43]

import numpy as np
# 创建矩阵
matrix = np.array([[1, 2], [3, 4]])
# 求逆矩阵
result = np.linalg.inv(matrix)
print(result)

import numpy as np
# 创建矩阵
matrix = np.array([[1, 2], [3, 4]])
# 计算矩阵的迹
result = np.trace(matrix)
print(result)

import numpy as np
# 创建两个向量
vector1 = np.array([1, 2])
vector2 = np.array([3, 4])
# 向量点积
result = np.dot(vector1, vector2)
print(result)

import numpy as np
# 创建向量
vector = np.array([1, 2, 3])
# 计算向量的L2范数
result = np.linalg.norm(vector)
print(result)

import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6], [7, 8]])
print(np.dot(a, b))
# [[19 22]
#  [43 50]]

import numpy as np
a = np.array([[1, 2], [3, 4]])
print(np.linalg.inv(a))
# [[-2.   1. ]
#  [ 1.5 -0.5]]

import numpy as np
a = np.array([[2, 3], [4, 5]])
b = np.array([5, 6])
x = np.linalg.solve(a, b)
print(x) # [-4.  5.]