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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus / Röpke, Gerd / Steeb, Willi-Hans

12 Issues per year


IMPACT FACTOR 2016: 1.432

Cite Score 2016: 1.35

SCImago Journal Rank (SJR) 2016: 0.368
Source Normalized Impact per Paper (SNIP) 2016: 0.594

Online
ISSN
1865-7109
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Volume 70, Issue 8 (Aug 2015)

Issues

Eigenvalue Problem, Spin Systems, Lie Groups, and Parameter Dependence

Willi-Hans Steeb
  • Corresponding author
  • International School for Scientific Computing, University of Johannesburg, Auckland Park 2006, South Africa
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Yorick Hardy
  • Department of Mathematical Sciences, University of South Africa, Johannesburg, South Africa, E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-05-26 | DOI: https://doi.org/10.1515/zna-2015-0139

Abstract

We study square matrices F(α) over ℂ with α∈ℝ, where the eigenvalues depend on the parameter α but not the eigenvectors, and vice versa, where the eigenvectors depend on the parameter α but not the eigenvalues. We derive sufficient conditions for such properties. Applications to Lie groups and spin systems are provided. Both normal and nonnormal matrices are investigated.

Keywords: Eigenvalue Problems; Lie Groups; Spin Systems

References

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About the article

Corresponding author: Willi-Hans Steeb, International School for Scientific Computing, University of Johannesburg, Auckland Park 2006, South Africa, E-mail:


Received: 2015-03-25

Accepted: 2015-04-26

Published Online: 2015-05-26

Published in Print: 2015-08-01


Citation Information: Zeitschrift für Naturforschung A, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2015-0139.

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