1. python求矩阵的转置

G1 = np.transpose(G)

>>> import numpy as np
>>> G = np.array([[1,0,0,1],[0,1,0,-1],[0,0,1,1]])
>>> G1=np.transpose(G)
>>> G1
array([[ 1,  0,  0],
       [ 0,  1,  0],
       [ 0,  0,  1],
       [ 1, -1,  1]])

2. python求矩阵乘法

G2 = np.dot(G,G1)

>>> import numpy as np
>>> G = np.array([[1,0,0,1],[0,1,0,-1],[0,0,1,1]])
>>> G1=np.transpose(G)
>>> G1
array([[ 1,  0,  0],
       [ 0,  1,  0],
       [ 0,  0,  1],
       [ 1, -1,  1]])
>>> G2 = np.dot(G,G1)
>>> G2
array([[ 2, -1,  1],
       [-1,  2, -1],
       [ 1, -1,  2]])

3. python求矩阵的逆

G3 = np.linalg.inv(G2)

>>> import numpy as np
>>> G = np.array([[1,0,0,1],[0,1,0,-1],[0,0,1,1]])
>>> G1=np.transpose(G)
>>> G1
array([[ 1,  0,  0],
       [ 0,  1,  0],
       [ 0,  0,  1],
       [ 1, -1,  1]])
>>> G2 = np.dot(G,G1)
>>> G2
array([[ 2, -1,  1],
       [-1,  2, -1],
       [ 1, -1,  2]])
>>> G3 = np.linalg.inv(G2)
>>> G3
array([[ 0.75,  0.25, -0.25],
       [ 0.25,  0.75,  0.25],
       [-0.25,  0.25,  0.75]])

4. python求矩阵的伪逆

K = np.linalg.pinv(J)

>>> import numpy as np
>>> J = np.array([[1,0,0,1],[1,1,0,0],[0,1,1,0],[0,0,1,1]])
>>> K = np.linalg.pinv(J)
>>> K
array([[ 0.375,  0.375, -0.125, -0.125],
       [-0.125,  0.375,  0.375, -0.125],
       [-0.125, -0.125,  0.375,  0.375],
       [ 0.375, -0.125, -0.125,  0.375]])

5 python求解矩阵的特征值

B = np.linalg.eigvals(A)

>>> A = np.mat("0 0 0; -1 1 -1; 1 -1 1") 
>>> A
matrix([[ 0,  0,  0],
        [-1,  1, -1],
        [ 1, -1,  1]])
>>> B = np.linalg.eigvals(A)
>>> B
array([2., 0., 0.])

6 python求解矩阵的特征值和特征向量

B,C = np.linalg.eig(A)

>>> A = np.array([[1,0,-1,0],[0,1,0,-1],[-1,0,1,0],[0,-1,0,1]])
>>> A
array([[ 1,  0, -1,  0],
       [ 0,  1,  0, -1],
       [-1,  0,  1,  0],
       [ 0, -1,  0,  1]])
>>> B,C = np.linalg.eig(A)
>>> B
array([2., 0., 2., 0.])
>>> C
array([[ 0.70710678,  0.70710678,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.70710678,  0.70710678],
       [-0.70710678,  0.70710678,  0.        ,  0.        ],
       [ 0.        ,  0.        , -0.70710678,  0.70710678]])

注： 这是返回单位化的特征向量