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1.6
1.6 Bases
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?
Examples:
Standard basis is ever basis is nice.
, polynomial
Theorem: Linear independence gives you unique representation.
Theorem: Span gives you span.
Theorem: Basis gives you both.
Examples:
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 then some subset of is a basis.