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

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