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content/notes/01-Vector-Spaces-and-Subspaces.md
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@ -6,12 +6,14 @@ tags:
- math202 - math202
--- ---
- ![pdf](https://www.maths.otago.ac.nz/webdata/resources/math202/2022_S2_Outline_Notes/Ch1.pdf?m=1657334841) - [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 - a vector space is a set whose elements conform to the eight axioms of scaling and additiveness
- e.g., - e.g.,
- ℝ², ℝ³, P₃ - ℝ², ℝ³, P₃
- In this course we focus on three main vector spaces - In this course we focus on three main vector spaces
- ℝⁿ, Pₙ, $M_{m\times n}$ - 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
- -