Linear Algebra › Section D · Vector spaces › Topic D.3
Linearly independent sets and bases
A basis is a spanning set with no waste: every vector it builds is built in only one way. This topic carries linear independence into general vector spaces and shows how to find bases for column spaces and null spaces.
In this topic
- Spanning without waste
- Linear independence in any vector space
- Independence among functions
- What a basis is
- The spanning set theorem
- Worked example: a basis for Col A
- Pivot columns of A, not of its echelon form
- Worked example: a basis for Nul A
- Two views of a basis
- Common mistakes to avoid
- Key takeaways
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