Eigenvalues of symmetric matrices over integral domains

Publikationstyp: Zeitschriftenartikel
Publikationsstatus: Published
Autor/innen: Kummer, Mario
Erscheinungsjahr: 2016
Erschienen in: Journal of Algebra ; 466 (2016). - S. 195-203. - ISSN 0021-8693. - eISSN 1090-266X
ArXiv-ID: arXiv:1511.01048
DOI (zitierfähiger Link): https://dx.doi.org/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.
Fachgebiet (DDC): 510 Mathematik
Schlagwörter: Real algebra; Number theory; Matrices
Kommentar zur Publikation: Serious error in previous version

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KUMMER, Mario, 2016. Eigenvalues of symmetric matrices over integral domains. In: Journal of Algebra. 466, pp. 195-203. ISSN 0021-8693. eISSN 1090-266X

@article{Kummer2016Eigen-37288, title={Eigenvalues of symmetric matrices over integral domains}, year={2016}, doi={10.1016/j.jalgebra.2016.07.024}, 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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