- Defintion: A basis is a linearly independent and spanning set. The dimension is the cardinality of the basis.
- Does it exist? Is it unique? Is there any invariant?
- Standard basis is ever basis is nice.
- Fn, polynomial
- Theorem: Linear independence gives you unique representation.
- Theorem: Span gives you span.
- Theorem: Basis gives you both.
- Do problem 3 in au17 final, both null and col
- In this course, in terms of basis, we are primarily interested in finite dimensional spaces.
- Theorem: If a space is finitely generated by S then some subset of S is a basis.