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Summary: Singular Value Decomposition
(SVD)
and
Generalized
Singular Value Decomposition
(GSVD)
Hervé Abdi1
1 Overview
The singular value decomposition (SVD) is a generalization of the
eigen-decomposition which can be used to analyze rectangular
matrices (the eigen-decomposition is defined only for squared ma-
trices). By analogy with the eigen-decomposition, which decom-
poses a matrix into two simple matrices, the main idea of the SVD
is to decompose a rectangular matrix into three simple matrices:
Two orthogonal matrices and one diagonal matrix.
Because it gives a least square estimate of a given matrix by
a lower rank matrix of same dimensions, the SVD is equivalent to
principal component analysis (PCA) and metric multidimensional
1
In: Neil Salkind (Ed.) (2007). Encyclopedia of Measurement and Statistics.
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