---
tags:
  - maths
---
# Field

-   Set on which addition and multiplication defined
	-   Behave same as on rational and real numbers
	-   Subtraction, division implied
-   Examples
	-   Rational numbers
	-   Real numbers
	-   Complex numbers
-   Any field can be used as scalars for a vector space
-   A commutative ring where 0 =/= 1 and all nonzero elements are invertible

## Vector Space
-   Set of vectors
	-   Can be added together and multiplied by scalar
		-   Can be scaled by complex numbers
			-   Part of definitions
		-   Must satisfy vector axioms