NumPy基础：线性代数

import numpy as np
from numpy.linalg import inv, qr, eig, det, pinv, svd, lstsq, solve
from numpy.matlib import randn, trace

x = np.array([[1,2,3],[4,5,6]])
y = np.array([[6,23],[-1,7],[8,9]])

print(x.dot(y)) # np.dot(x,y)
'''
1*6+2*(-1)+3*8=28 
[[ 28  64]   
 [ 67 181]]
'''

x = np.array([[1,2,3],[4,5,6],[7,8,9]])
# 以一维数组的形式返回方阵对角线元素
print(np.diag(x))  # [1 5 9]

# 矩阵乘法
print(np.dot(x,y))
'''
[[ 30  36  42]
 [ 66  81  96]
 [102 126 150]]
'''

# 计算对角线元素的和
print(trace(x)) # 15

# 计算矩阵行列式
det(x)


# 计算方阵的本征值和本征向量
eig(x)

# 计算方阵的逆
inv(x)

# 就算矩阵的Moose-Penrose的逆
pinv(x)

# 计算QR分解
qr(x)

# 计算奇异值分解（SVD）
svd(x)

# 解线性方程组Ax = b ，其中A为一个方阵
A = np.array([[1,1,1],[0,2,5],[2,5,1]])
x = np.array([4.29411765,4.17647059,-2.47058824])
b = np.array([6,-4,27])
print(solve(A,b)) # [4.29411765,4.17647059,-2.47058824]


# 计算Ax = b的最小乘解
print(lstsq(A,b))