NumPy线性代数函数库linalg

NumPy线性代数函数库linalg

NumPy模块中提供了线性代数函数库linalg，该库包含了线性代数所需的所有功能

1. 求方阵的行列式

numpy.linalg.det()可以计算方阵的行列式

import numpy as np
A = np.array([[1,2],
              [1,1]])
try:
    A_det = np.linalg.det(A)
except Exception as e:
    print(e)
else:
    print("det(A) = ", A_det)

2. 求方阵的逆矩阵

numpy.linalg.inv()可以计算方阵的逆矩阵

import numpy as np
A = np.array([[1,2],
              [1,1]])
try:
    A_inv = np.linalg.inv(A)
except Exception as e:
    print(e)
else:
    print("The inverse matrix of A is")
    print(A_inv)

3. 求解有唯一解的线性方程组

numpy.linalg.solve()可以求解有唯一解的线性方程组Ax=b

import numpy as np
A = np.array([[1,2],
              [1,1]])
b = np.array([[1,0],
              [0,1]])
try:
    X = np.linalg.solve(A, b)
except Exception as e:
    print(e)
else:
    print("The solution of AX=b is")
    print(X)

4. 求方阵的特征值和特征向量

numpy.linalg.eig()可以计算方阵的特征值λ和特征向量X0，即(A-λE)X0=0，其中E为单位矩阵

import numpy as np
A = np.array([[1, 2],
              [1, 1]])
try:
    A_lambda, X0 = np.linalg.eig(A)
except Exception as e:
    print(e)
else:
    print("The eigenvalues of A has", A_lambda)
    print("The eigenvector of A has")
    print(X0)