numpy中*，np.multiply和np.dot辨析

1 总结 向量的内积（点乘）：np.dot(a,b)=a@b 向量的外积（叉乘）：np.cross(a,b) 向量元素对应位置相乘：np.multiply(a,b)=a*b

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矩阵点乘——对应元素相乘：np.multiply(a,b)=a*b 矩阵叉乘——矩阵乘法规则运算：np.dot(a,b)=a@b 2 向量 2.1 向量的内积（点乘）：np.dot(a,b)=a@b

a = [ a 1 , a 2 , a 3 ] a=[a_1,a_2,a_3] a=[a1​,a2​,a3​]
b = [ b 1 , b 2 , b 3 ] b=[b_1, b_2,b_3] b=[b1​,b2​,b3​]
a ⋅ b = a 1 b 1 + a 2 b 2 + a 3 b 3 a·b=a_1b_1+a_2b_2+a_3b_3 a⋅b=a1​b1​+a2​b2​+a3​b3​

2.2 向量的外积（叉乘）：np.cross(a,b)

2.4 向量元素对应位置相乘：np.multiply(a,b)=a*b 2.3 示例

x = np.array([1, 2, 3])
y = np.array([6, 7, 8])

print("-" * 20, "np.cross(x,y)", "-" * 20)
print(np.cross(x, y))

print("-" * 20, "x*y", "-" * 20)
print(x * y)

print("-" * 20, "np.multiply(x,y)", "-" * 20)
print(np.multiply(x, y))

print("-" * 20, "np.dot(x,y)", "-" * 20)
print(np.dot(x, y))

print("-" * 20, "x@y", "-" * 20)
print(x @ y)

3 矩阵 3.1 矩阵点乘——对应元素相乘：np.multiply(a,b)=a*b

矩阵点乘要求两矩阵为同型矩阵，即两个矩阵的行数与列数都相同

3.2 矩阵叉乘——矩阵乘法规则运算：np.dot(a,b)=a@b

矩阵叉乘中， 前者的列数必须和后者的行数相等

3.3 示例

a = np.array([[1, 2], [3, 4]])
b = np.array([[3, 4], [5, 6]])
print("a=n", a)
print("b=n", b)

print("-" * 20, "np.cross(a,b)", "-" * 20)
print(np.cross(a, b))

print("-" * 20, "a*b", "-" * 20)
print(a * b)

print("*" * 20, "np.multiply(a,b)", "-" * 20)
print(np.multiply(a, b))

print("*" * 20, "np.dot(a,b)", "-" * 20)
print(np.dot(a, b))

print("-" * 20, "a@b", "-" * 20)
print(a @ b)
print(a @ b)