---
title: "01-Vector-Spaces-and-Subspaces"
aliases: 
tags: 
- lecture
- math202
---

- [pdf](https://www.maths.otago.ac.nz/webdata/resources/math202/2022_S2_Outline_Notes/Ch1.pdf?m=1657334841)

- a vector space is a set whose elements conform to the eight axioms of scaling and additiveness
- e.g.,
	- ℝ², ℝ³, P₃
- In this course we focus on three main vector spaces
	- ℝⁿ, Pₙ, $M_{m\times n}$ 

- a vector subspace is a subset of a vector space whose elements (which are vectors) are additively and multipicatively closed and contain the zero vector

complex numbers: 

$The complex number z has the from a+b i where a,b \element$