Unit 4 Summary

Linear Algebra for Machine Learning · Axiom Academy

Systems of Equations & Least Squares Elementary row operations preserve solution sets Gaussian elimination transforms complexity into structure (triangular form) LU decomposition trades upfront cost for savings on multiple systems Overdetermined systems require least squares, not exact solutions Normal equations solve least squares by converting to a square system Residual orthogonality ( ) is the key principle of least squares Regression is projection: finding the point in Col(A) closest to b Polynomial fitting uses Vandermonde matrices within the least squares framework Machine Learning: Linear regression, logistic regression, neural networks all use least squares or its variants Data Science: Fitting models to data, feature selection, predictive modeling Engineering: Finite element analysis, structural mechanics, circuit analysis Economics: Econometric modeling, time series analysis, forecasting Physics: Curve fitting to experimental data, inverse problems Computer Graphics: Polynomial interpolation, spline fitting, mesh optimization Signal Processing: Filtering, denoising, pattern recognition Finance: Portfolio optimization, risk modeling, regression-based pricing

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