Linear Algebra
Overview
Section titled “Overview”Linear algebra problems reward finding the right invariant: rank, determinant, trace, nullity, eigenvalues, or a useful basis. When a statement is coordinate-heavy, try translating it into a map between vector spaces.
Checklist
Section titled “Checklist”- Identify the vector space and the linear map.
- Check rank-nullity and dimension constraints.
- Look for invariant subspaces.
- Use determinant and trace when eigenvalues matter.
- Change basis if the current coordinates hide the structure.
Common moves
Section titled “Common moves”- Prove injective equals surjective in finite dimensions.
- Diagonalize or triangularize when possible.
- Use minimal polynomials for repeated matrix identities.
- Convert systems of equations into matrix rank statements.
Practice problems
Tags: linear-algebra
| Done | Problem | Source | Difficulty | Tags |
|---|---|---|---|---|
| Starter Linear Algebra Problem | Boilerplate | 5 | linear-algebra, matrices |