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On the Use of Eigenvalues and Eigenvectors in the Phase Problem

On the Use of Eigenvalues and Eigenvectors in the Phase Problem Karle-Hauptman matrices may be used in an algebraic approach to the phase problem. When eigenvalues and eigenvectors are used, it is possible to obtain structural information from Karle-Hauptman matrices of orders greater than N, despite the fact that the determinants are zero. In this paper, the properties of large Karle-Hauptman matrices are examined in the infinite and non-infinite cases. The characteristics of electron densities corresponding to separate eigenvectors are examined. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

On the Use of Eigenvalues and Eigenvectors in the Phase Problem

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On the Use of Eigenvalues and Eigenvectors in the Phase Problem

van der Plas, J.L; de Graaff, R.A.G; Schenk, H
Acta Crystallographica Section A: Foundations of Crystallography , Volume 54 (3): 262 – May 1, 1998

Abstract

Karle-Hauptman matrices may be used in an algebraic approach to the phase problem. When eigenvalues and eigenvectors are used, it is possible to obtain structural information from Karle-Hauptman matrices of orders greater than N, despite the fact that the determinants are zero. In this paper, the properties of large Karle-Hauptman matrices are examined in the infinite and non-infinite cases. The characteristics of electron densities corresponding to separate eigenvectors are examined.

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Publisher
International Union of Crystallography
Copyright
Copyright (c) 1998 International Union of Crystallography
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767397013597
Publisher site
See Article on Publisher Site

Abstract

Karle-Hauptman matrices may be used in an algebraic approach to the phase problem. When eigenvalues and eigenvectors are used, it is possible to obtain structural information from Karle-Hauptman matrices of orders greater than N, despite the fact that the determinants are zero. In this paper, the properties of large Karle-Hauptman matrices are examined in the infinite and non-infinite cases. The characteristics of electron densities corresponding to separate eigenvectors are examined.

Journal

Acta Crystallographica Section A: Foundations of Crystallography – International Union of Crystallography

Published: May 1, 1998

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