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On an SVD‐free approach to the complementarity and coupling theory A note on the elimination of unknowns in sums of dyadic products
Author(s) -
Neymeyr Klaus,
Sawall Mathias
Publication year - 2016
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2765
Subject(s) - singular value decomposition , complementarity (molecular biology) , affine transformation , linear complementarity problem , mathematics , linear algebra , algebra over a field , factorization , matrix decomposition , pure mathematics , nonlinear system , algorithm , eigenvalues and eigenvectors , genetics , physics , geometry , quantum mechanics , biology
The partial knowledge of the factors in a multivariate curve resolution problem can simplify the factorization problem. The complementarity and coupling theory as published in 2012 provides precise mathematical conditions for certain unknown parts of the factors. These constraints are based on a singular value decomposition of the data matrix; they have the form of linear or affine linear spaces which contain the unknown parts of the pure component factors. This paper presents a new and simple singular value decomposition‐free form of the complementarity and coupling theory. The derivation of these theorems is based on elementary arguments of linear algebra. The new mathematical form of the theory allows its easy and straightforward applicability. Copyright © 2015 John Wiley & Sons, Ltd.