Linear Algebra › Section D · Vector spaces › Topic D.5
The dimension of a vector space
A space can have many bases, but every basis of it has the same number of vectors. That number, the dimension, measures how many independent directions the space has, and it makes many questions about bases almost automatic.
In this topic
- Counting independent directions
- Too many vectors means dependence
- Every basis has the same size
- Dimensions of familiar spaces
- Worked example: the dimension of a subspace
- Subspaces of a finite-dimensional space
- The basis theorem
- Worked example: a basis of quadratics
- Dimensions of Nul A and Col A
- Common mistakes to avoid
- Key takeaways
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