Axler 3.C

matricies!!!!

Key Sequence

• matricies exist, you can add them, scalarly multiply them, and actually multiply them
• they can represent Linear Maps by showing where they take basis
• unsurprisingly, the set of matricies of a shape is a vector space

New Definitions

• matricies
  • matrix of Linear Map
  • matrix addition and scalar multiplications
  • matrix multiplication
• \(\mathbb{F}^{m,n}\)

Results and Their Proofs

• sums and scalar multiplication of matricies, and why they work to represent Linear Maps
• \(\mathbb{F}^{m,n}\) is a vector space

Interesting Factoids

its literally matricies