A=np.array([[1,2,3],[4,5,6],[7,8,9]])

B=np.array([[3,1,5],[9,2,4],[6,8,7]])

X=np.array([4,3,1])

Y=np.array([7,0,2])

np.dot(A@X,B@Y)
Out[21]: 6446

np.dot(A@X,np.array([Y])@B.T)
Traceback (most recent call last):

  File "<ipython-input-22-5de65b47e121>", line 1, in <module>
    np.dot(A@X,np.array([Y])@B.T)

ValueError: shapes (3,) and (1,3) not aligned: 3 (dim 0) != 1 (dim 0)




np.dot(A@X,Y.T@B.T)
Out[23]: 6446

np.dot(A@X,Y.T@B)
Out[24]: 4269

np.dot(A@X,Y@B.T)
Out[25]: 6446

np.dot(X,Y@A@B.T)
Out[26]: 3006

np.dot(X,Y@A.T@B.T)
Out[27]: 3918

np.dot(X,Y@B.T@A.T)
Out[28]: 5098

np.dot(X,Y@B.T@A)
Out[29]: 6446

np.linalg.inv(A)
Out[30]: 
array([[ 3.15251974e+15, -6.30503948e+15,  3.15251974e+15],
       [-6.30503948e+15,  1.26100790e+16, -6.30503948e+15],
       [ 3.15251974e+15, -6.30503948e+15,  3.15251974e+15]])

np.dot(X,(A@B@Y))
Out[31]: 5098

np.dot(X,(A@B@Y).T)
Out[32]: 5098

Y@B.T@A.T
Out[33]: array([ 341,  815, 1289])

(A@B@Y).T
Out[34]: array([ 341,  815, 1289])

np.dot(X,Y@B.T@A)
Out[35]: 6446

np.dot(X,(A@B@Y).T)
Out[36]: 5098

Z1=(A@B@Y).T


np.dot(X,Z1)
Out[38]: 5098

Z2=Y@B.T@A.T

np.dot(X,Z2)
Out[40]: 5098

np.dot(X,Y@B.T@A)
Out[41]: 6446

np.dot(X,Y@B.T@A.T)
Out[42]: 5098

A=np.array([[1,2,3],[9,9,699],[7,8,9]])

np.dot(A@X,Y.T@B.T)
Out[44]: 57921

np.dot(X,Y@B.T@A)
Out[45]: 57921

np.dot(Y.T,B.T@A@X)
Out[46]: 57921

AX.* (BY)‘=AX.* Y’B’=X.*(Y’B’A)=Y’B’AX

这里的 ’ 表示矩阵的转置