Linear Algebra › Section F · Orthogonality and least squares › Topic F.8
Applications of inner product spaces
Choosing the right inner product turns practical problems into projections: fitting data whose points deserve different amounts of trust, tracking trends with polynomials that do not interfere with each other, and building a function out of sine and cosine waves.
In this topic
- One idea, three applications
- Weighted least squares
- Worked example: trusting one point more
- Trend analysis with orthogonal polynomials
- Worked example: a quadratic trend
- Fourier approximation
- The Fourier coefficients
- Worked example: approximating a V shape
- Measuring the error
- Common mistakes to avoid
- Key takeaways
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