Singular Value Decomposition: A Geometric Rediscovery, Where Proofs Become Algorithms
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 $A = UΣV^T$ and justifies it via the spectral theorem applied to $A^T A$. This is correct but unilluminating, since it assumes a powerful theorem to reach a result that is, in the end, about ellipses. Part I reverses the order. A linear map sends the un...
| Authors | Paul Agron |
|---|---|
| Primary category | cs.LG |
| Published | 6 October 2026 |
| Last updated at source | 6 October 2026 |
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