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?
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.