Linear Algebra › Section D · Vector spaces › Topic D.4
Coordinate systems
Once a space has a basis, every vector in it can be described by a list of numbers, its coordinates. That list turns polynomials, matrices and planes in space into ordinary vectors in Rⁿ, where row reduction does the work.
In this topic
- Why a basis gives coordinates
- The unique representation theorem
- Coordinates and the coordinate vector
- Worked example: coordinates in the plane
- The change-of-coordinates matrix
- The coordinate mapping
- Worked example: coordinates of a polynomial
- Testing polynomials with coordinates
- Coordinates on a plane in space
- Common mistakes to avoid
- Key takeaways
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