Linear Algebra › Section H · The geometry of vector spaces › Topic H.3
Convex combinations
Restrict the weights of an affine combination to be non-negative and lines shrink to segments, planes to triangles. These convex combinations describe blends, averages and centres of mass, and they define convex sets, the shapes at the heart of optimisation.
In this topic
- From lines to segments
- Definition and the convex hull
- Convex sets
- The smallest convex set containing S
- Worked example: inside or outside a triangle?
- Carathéodory's theorem
- Worked example: removing a point
- Blends and centres of mass
- Common mistakes to avoid
- Key takeaways
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