• Table of Contents

Digression

Some basic algebraic objects that will capture the most fundamental properties of vector spaces.

• We’ll see this lets us naturally extend it to complex numbers

Keep in mind:

1. “Vectors” live in vector spaces
2. “Scalars” live in fields

Groups

Fields

Complex Numbers

Vector Spaces

This section goes over the algebraic properties of a vector space. We generalize some basic principles which correspond to what’s loosely called linear structure

• In short: the minimal properties that people believe makes things "vector-ey”

Vector Spaces over Fields

Subspaces

Operations on Vector Spaces

Linear Combinations