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.
Note: 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.
Source:
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)