Svd

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Eckart and Young settled which rank-k matrix is closest to yours — your own truncated SVD — and said nothing about which k. The scree plot fills that gap with a judgement about a shape and no reference distribution, and on a matrix with no structure in it that judgement returns a number every time....