10115 IUPAC Gold Book - singular value decomposition 10.1351/goldbook.10115 10115 current initialism: SVD 1 A factorization of an \(m \times n\) matrix (\(\boldsymbol{M}\)) such that \(\boldsymbol{M} = \boldsymbol{U}\boldsymbol{\Sigma} \boldsymbol{V}^{T}\), where \(\boldsymbol{U}\) is an \(m \times m\) matrix, \(\boldsymbol{\Sigma}\) is a \(m \times n\) matrix and \(\boldsymbol{V}^{\rm{T}}\) is a \(n \times n\) matrix. If \(\boldsymbol{M}\) is a data matrix with \(m\) objects and \(n\) variables, the matrix \(\boldsymbol{U}\) is the scores matrix, the diagonal of \(\boldsymbol{\Sigma}\) contain the square roots of the eigenvalues and \(\boldsymbol{V}\) is the loadings matrix. data matrix https://goldbook.iupac.org//terms/view/10047 loadings https://goldbook.iupac.org//terms/view/10096 scores https://goldbook.iupac.org//terms/view/10112 PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 425 (https://doi.org/10.1515/pac-2015-0605) https://goldbook.iupac.org/terms/view/10115/html https://goldbook.iupac.org/terms/view/10115/json https://goldbook.iupac.org/terms/view/10115/plain Citation: 'singular value decomposition' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10115 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-07-25T16:30:38+00:00