Singular Value Decomposition: A Geometric Rediscovery, Where Proofs Become Algorithms
The Singular Value Decomposition (SVD) is geometrically rediscovered as a construction method rather than just a theorem. It starts by showing how a linear map transforms the unit circle into an ellipse, proving that finding the axes involves an algorithm of maximizing stretch and recursion. This geometric process directly yields algorithms used in machine learning, such as principal component analysis and PageRank.