Linear Algebra: Vector Basics

Linear Algebra Introduction

This is the first section I’m writing on Linear Algebra. I’m working through the Khan Academy course and looking at various other references like Wikipedia and Wolfram Alpha as needed. Utlimately, I want to be able to get a better handle on rendering graphics. Currently, I just know it needs linear algebra. Machine learning is a secondary benefit, as it hasn’t interested me too much.

Vector Definition

Vectos are mathematical objects that are defined by their magnitude and direction. This definition is a good starting point, because it keeps it simple. Vectors can be added together and scaled by constants to create new vectors. Vectors are often represented in a 2d Euclidean plane and often start at the origin at (0,0), but this is just a convention. Vectors exist independently of their coordinate system.

Vector Notation

Vectors like $\overrightarrow{v}$ can be written as coordinate pairs: $\left(x,y\right)$, as components of unit vectors: $î+ĵ$, or as a magnitude and a direction: $\left(r,\theta \right)$.