MathematicsCoreMTH-LINALG-159
Basis & Dimension
basis characterization, dimension theorem, coordinate vectors
- Difficulty
- 3 / 5
- Importance
- 5 / 5
- Study time
- 3–6 h
- Kind of work
- Mixed
Why it matters
Gives every vector space a coordinate system; dimension is the fundamental invariant.
Where it is used
Compression (PCA/SVD), solving systems, signal representation (Fourier basis).
How you know you have learned it
Complete 3 independent examples correctly + explain common failure modes.
Resources
- Linear Algebra Done Right — Sheldon Axler Book
- Linear Algebra Done Right — Sheldon Axler Book
- Introduction to Linear Algebra — Gilbert Strang Book