nparray变量，如何利用 .dot() 做向量点积和矩阵乘积计算？

import numpy as np
x = np.array([1,2,3])   # [1 2 3]
y = np.arange(6,3,-1)   # [6 5 4]
print(x,y)              # 形状 需要一致

a1 = x @ y
a2 = y @ x
print(a1,a2)            # 28 28

# 1*6 + 2*5 + 3*4 = 6 + 10 + 12 = 28

b1 = np.dot(x,y)
b2 = np.dot(y,x)
print(b1,b2)            # 28 28

c1 = x.dot(y)
c2 = y.dot(x)
print(c1,c2)            # 28 28

import numpy as np
x = np.array([1,2,3])                  # [1 2 3]
y = np.arange(6,3,-1).reshape((3,1))   # [[6] [5] [4]]

print(x,y)              
print(x.shape,y.shape)  # 这里的形状并不一致，(3,) (3, 1)。但是属于类似的形状

a1 = x @ y              # [28]
# a2 = y @ x            # ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 3 is different from 1)

b1 = np.dot(x,y)        # [28]
# b2 = np.dot(y,x)      # ValueError: shapes (3,1) and (3,) not aligned: 1 (dim 1) != 3 (dim 0)

c1 = x.dot(y)           # [28]
# c2 = y.dot(x)         # ValueError: shapes (3,1) and (3,) not aligned: 1 (dim 1) != 3 (dim 0)

[ [1, 2], [3, 4], [5, 6] ]
[ [7, 8], [9, 10] ]

[[ 25  28]
 [ 57  64]
 [ 89 100]]

import numpy as np
x = np.array([ [1, 2], [3, 4], [5, 6] ])
y = np.array([ [7, 8], [9, 10] ])

print(x,y)              
print(x.shape,y.shape)  # 这里的形状并不一致

'''
[[1 2]
 [3 4]
 [5 6]] 

[[ 7  8]
 [ 9 10]]

(3, 2) (2, 2)
'''

a1 = x @ y
# a2 = y @ x          # ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 3 is different from 2)

b1 = np.dot(x,y)
# b2 = np.dot(y,x)    # ValueError: shapes (2,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)

c1 = x.dot(y)
# c2 = y.dot(x)       # ValueError: shapes (2,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)

'''
[[ 25  28]
 [ 57  64]
 [ 89 100]]
'''