Numpy docs talks about the difference between the product operator and the matrix operator.

Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the @ operator (in python >=3.5) or the dot

Question: What is the difference between the operator acting elementwise vs on the matrix?

How would it change the outcome?

CodePudding user response：

Say we've got two matrices:

a = [ p q ]
    [ r s ]

b = [ w x ]
    [ y z ]

Element-wise product means:

a * b = [ p*w  q*x ]
        [ r*y  s*z ]

Matrix product means:

a @ b = [ (p*w) (q*y)  (p*x) (q*z) ]
        [ (r*w) (s*y)  (r*x) (s*z) ]

When literature in math, machine learning etc talks about "matrix multiplication", this matrix product is what is meant. Note that a @ b is not the same as b @ a.