Linear Algebra › Section F · Orthogonality and least squares › Topic F.7
Inner product spaces
Length, angle and projection need only a few rules to work. Any operation that obeys those rules gives a vector space geometry, which lets us measure how far apart two functions or polynomials are and find the best approximation to one by others.
In this topic
- Geometry beyond Rn
- The four axioms
- A weighted inner product on R2
- Polynomials: an inner product by evaluation
- Worked example: Gram-Schmidt on polynomials
- Functions: an inner product by integration
- Worked example: the best line for a curve
- Everything carries over
- Proving Cauchy-Schwarz and the triangle inequality
- Common mistakes to avoid
- Key takeaways
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