Singular value decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any
Singular value decomposition - Wikipedia Jump to content From Wikipedia, the free encyclopedia Matrix decomposition This article includes a list of references , related reading , or external links , but its sources remain unclear because it lacks inline citations . Please help improve this article by introducing more precise citations. ( March 2026 ) ( Learn how and when to remove this message ) Illustration of the singular value decomposition UΣV * of a real 2 × 2 matrix M . Top: The action of M , indicated by its effect on the unit disc D and the two canonical unit vectors e 1 and e 2 . Left
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related reading
- Singular Value Decomposition as Simply as Possiblegregorygundersen.com
- Six (and a half) intuitions for SVD — LessWronglesswrong.com
- https://www.deeplearningbook.org/contents/linear_algebra.htmldeeplearningbook.org
- pca - What is the intuition behind SVD? - Cross Validatedstats.stackexchange.com
- Matrix Singular Value Decomposition (SVD) Using the Jacobi Algorithm from Scratch JavaScript - James D. McCaffreyJames D. McCaffreyjamesmccaffrey.wordpress.com
- dimensionality reduction - Relationship between SVD and PCA. How to use SVD to perform PCA? - Cross Validatedstats.stackexchange.com
- Pen and Paper Exercises in Machine Learningarxiv.org
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- [1305.5870] The Optimal Hard Threshold for Singular Values is 4/sqrt(3)arxiv.org