---
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
