Notes - Linear Algebra I MT22, Chapter 6
- [[Course - Linear Algebra I MT22]]^{U}
- Content covered:
- Prove a linear map is invertible if and only if it is bijective (Prop. 154)
- Prove there exists an invertible linear map between two finite dimensional vector spaces if they have the same dimension. (Prop. 156)
- Prove lots of properties about the kernel and image relating to subspaces (Prop. 159)
- Prove the rank nullity theorem (The. 162).
Flashcards
What’s the useful inequality about the nullity composition of two linear maps?
\[\text{null}(ST) \le \text{null}(S) + \text{null}(T)\]
What’s the useful inequality about the rank of the sum of two linear maps?
\[\text{rank}(S + T) \le \text{rank}(S) + \text{rank}(T)\]