Publikation: Eigenvalues of symmetric matrices over integral domains
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2016
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Journal of Algebra. 2016, 466, pp. 195-203. ISSN 0021-8693. eISSN 1090-266X. Available under: doi: 10.1016/j.jalgebra.2016.07.024
Zusammenfassung
Given an integral domain A we consider the set of all integral elements over A that can occur as an eigenvalue of a symmetric matrix over A. We give a sufficient criterion for being such an element. In the case where A is the ring of integers of an algebraic number field this sufficient criterion is also necessary and we show that the size of matrices grows linearly in the degree of the element. The latter result settles a questions raised by Bass, Estes and Guralnick.
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510 Mathematik
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Real algebra; Number theory; Matrices
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KUMMER, Mario, 2016. Eigenvalues of symmetric matrices over integral domains. In: Journal of Algebra. 2016, 466, pp. 195-203. ISSN 0021-8693. eISSN 1090-266X. Available under: doi: 10.1016/j.jalgebra.2016.07.024BibTex
@article{Kummer2016Eigen-37288,
year={2016},
doi={10.1016/j.jalgebra.2016.07.024},
title={Eigenvalues of symmetric matrices over integral domains},
volume={466},
issn={0021-8693},
journal={Journal of Algebra},
pages={195--203},
author={Kummer, Mario},
note={Serious error in previous version}
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Serious error in previous version
