矩阵乘法.dot 以及 *

a1 = np.array([[1,2,1], [2,3,4]])  #.dot在双方是二位数组即矩阵时为正常的矩阵运算
b1 = np.array([1,2,3])             #（*）则可以应用于矩阵与向量的运算，矩阵里的元素乘以向量对应位置的元素
a1.dot(b1),b1*a1

(array([ 8, 20]),
 array([[ 1,  4,  3],
        [ 2,  6, 12]]))

a1 = np.array([[1,2,1], [2,3,4],[2,3,4]]) #.dot在有一方为向量时，则为点积运算
b1 = np.array([1,2,3]) 
c = a1.dot(b1)
c.shape,c

((3,), array([ 8, 20, 20]))

a1 = np.array([[1,2,1], [2,3,4],[2,3,4]] 
b1 = np.array([1,2,3])             
c = a1*b1
c.shape,c

((3, 3),
 array([[ 1,  4,  3],
        [ 2,  6, 12],
        [ 2,  6, 12]]))

a1 = np.array([[1,2,1], [2,3,4],[2,3,4]]) 
b1 = np.array([[1],[2],[3]])            
c = a1*b1
c.shape,c

((3, 3),
 array([[ 1,  2,  1],
        [ 4,  6,  8],
        [ 6,  9, 12]]))