Löwdin's canonical orthogonalization: Getting round the restriction of linear independence
Löwdin's canonical orthogonalization procedure can be useful in organizing large data sets, but it is applicable only to a set of linearly independent vectors. This places a serious constraint for there can be at most n linearly‐independent vectors in an n‐dimensional space. We propose two ways...
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Veröffentlicht in: | International journal of quantum chemistry 2004, Vol.99 (6), p.882-888 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Löwdin's canonical orthogonalization procedure can be useful in organizing large data sets, but it is applicable only to a set of linearly independent vectors. This places a serious constraint for there can be at most n linearly‐independent vectors in an n‐dimensional space. We propose two ways of getting round this restriction so that Löwdin's procedure can be used to find the vector along which all the given vectors—any number of them in a space of arbitrary dimensionality—project maximally. Under these conditions, this orthogonalization procedure is equivalent to the principal component analysis. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 |
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ISSN: | 0020-7608 1097-461X |
DOI: | 10.1002/qua.20136 |