Linear Algebra › Section F · Orthogonality and least squares › Topic F.5
Least-squares problems
Measurements carry errors, so a system with more equations than unknowns usually has no exact solution. Least squares finds the next best thing: the vector that comes as close as possible to solving it, using the projections of this section.
In this topic
- When Ax = b has no solution
- What a least-squares solution is
- The geometry: project b onto Col A
- The normal equations
- Worked example: a 3 × 2 inconsistent system
- When the solution is unique
- Using a QR factorisation
- Worked example: least squares by QR
- A short history
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…