Projections, Least Squares & Numerical Stability

Connect least squares to orthogonal projection, residual geometry and reliable numerical computation. Practice projector formulas, QR solving, conditioning, basis changes and the correlation bound. Prerequisites: vectors, matrix products, rank and inverses. Progress from geometric calculations to rank-deficient fits, stability tradeoffs and the limits of what numerical accuracy establishes.

Further reading: Orthogonal projection, QR and regression.