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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:International journal of quantum chemistry 2004, Vol.99 (6), p.882-888
Hauptverfasser: Naidu, A. Ramesh, Srivastava, Vipin
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
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
ISSN:0020-7608
1097-461X
DOI:10.1002/qua.20136