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

### Like this:

Like Loading...

*Related*