Python/Numpy What's it called / how do you represent that operation where you multiply each element of two vectors?

Question

For example, suppose I have:

x = array([1, 2, 3])
y = array([4, 5, 6])

Standard "array multiplication" in python does z = x * y = array([4, 10, 18]). In matlab, to get the same effect, you do *. IIRC.

What is this operation called, and which symbol is used to represent it?

Answer 1

It is the Hadamard product represented with an open circle: http://en.wikipedia.org/wiki/Matrix_multiplication#Hadamard_product

Answer 2

It seems to me you are after the expression S = sum_i( x_i * y_i)? That is called the inner product. From numpy documentation:

from numpy import *
x = array([1,2,3])
y = array([2,2,2])
inner(x,y)          <-- Should give 1*2 + 2*2 + 3*2 = 12

The operation you have illustrated, and what you get with .* in matlab, is called a Schur/Hadamard product, often a small open circle is used as symbol. Since this is what you get with the normal '*' operator in numpy I doubt there is a separate Schur function.

Answer 3

Actually there are three different ways to multiply all the elements of two vectors.

The first one, the inner or dot product, returns a scalar.

The second one, the cross product, returns a vector.

The third one, the tensor product, returns a second-order tensor.

I'm sure you mean the first one, because it's familiar to most people, but I thought it'd be good to post this for the sake of completeness.