quartz/content/notes/01-Vector-Spaces-and-Subspaces.md

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

• pdf

• 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