concept inner product in category python

This is an excerpt from Manning's book Math for Programmers: 3D graphics, machine learning, and simulations with Python MEAP V11. Login to get full access to this book.

The dot product (also called the inner product) is an operation on two vectors that returns a scalar. In other words, given two vectors u and v, the result of u ∙ v is a real number. The dot product works on vectors in 2D, 3D, or any number of dimensions. You can think of it as measuring “how aligned” the pair of input vectors are. Let’s first look at some vectors in the x,y plane and show their dot products to give you some intuition for how this operation works.

Analogously, we can take a special inner product of a periodic function with a sine or cosine function to find a component associated with that function. The inner product for periodic functions is a definite integral taken over a specified range; in our case, from zero to one.