Linear Algebra › Section D · Vector spaces › Topic D.7
Change of basis
The same vector has different coordinates in different bases. A single matrix translates coordinates from one basis to another, and choosing the right basis can turn a messy problem into a simple one.
In this topic
- One vector, many descriptions
- The change-of-coordinates matrix
- Why the formula holds
- Computing it in Rⁿ
- Worked example: two bases of the plane
- Going back the other way
- Worked example: polynomials
- Why change basis at all
- Common mistakes to avoid
- Key takeaways
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