Linear Algebra › Section H · The geometry of vector spaces › Topic H.1
Affine combinations
Lines and planes that miss the origin are not subspaces, yet they are just as simple. Affine combinations, linear combinations whose weights add to 1, describe them exactly and do not depend on where the origin is, which is why geometry and computer graphics rely on them.
In this topic
- Points rather than vectors
- Definition and the affine hull
- Why the weights add to 1
- Worked example: testing membership in a plane
- Affine sets
- Flats: translated subspaces
- Homogeneous forms
- Worked example: using homogeneous forms
- Common mistakes to avoid
- Key takeaways
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