Singular Value Decomposition: A Geometric Rediscovery, Where Proofs Become Algorithms

Excerpt

arXiv:2610.08565v1 Announce Type: new Abstract: This article is a geometric rediscovery of the singular value decomposition, with a further claim: the construction it builds is the machinery behind much of machine learning. The same argument that answers an idle question about ellipses is the algorithm behind principal component analysis, kernel methods, and PageRank, and it is not only the results that transfer but the proofs themselves, run as procedures. The usual introduction states $A = U\S