Linear Algebra › Section H · The geometry of vector spaces › Topic H.4
Hyperplanes
A line divides the plane in two, and a plane divides space in two. Hyperplanes do the same job in any number of dimensions, which makes them the natural tool for describing boundaries, sorting data into classes and proving that two convex sets can be pulled apart.
In this topic
- Dividing space in two
- Linear functionals and the implicit description
- Half-spaces
- Worked example: a plane through three points
- Worked example: a hyperplane in four dimensions
- Explicit and implicit descriptions
- Separating hyperplanes
- Worked example: separating two point sets
- Common mistakes to avoid
- Key takeaways
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