Linear Algebra › Section B · Matrix algebra › Topic B.9
Dimension and rank
A basis turns a subspace into a coordinate system, and the number of vectors in it, the dimension, measures how big the subspace is. Counting dimensions gives the rank theorem, a simple equation that answers many questions about a matrix without solving anything.
In this topic
- Counting directions
- Coordinates relative to a basis
- Worked example: coordinates on a plane
- Dimension
- Rank and nullity
- The rank theorem
- Worked example: using the rank theorem
- The basis theorem
- Rank and the invertible matrix theorem
- Common mistakes to avoid
- Key takeaways
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