# Review of Linear Algebra for Machine Learning

Data is often represented by vectors with d scalar features

Definition 1. The inner product of two vectors x and y is



Note that   , that is


Definition 2.

The Euclidean Norm of vector x is ||x||



Note that

If ||x|| = 1, then x is normalized

Otherwise, we can normalize x to x’ as follows



Definition 3.

Vector x and y are orthogonal, if their scalar product is zero.



The angle between two vectors x and y is    if



Geometric interpretation is shown below

Note that the orthogonal projection of y onto x is