Eigenvalues of symmetric matrices over integral domains
| Type of Publication: | Journal article |
| Publication status: | Published |
| Author: | Kummer, Mario |
| Year of publication: | 2016 |
| Published in: | Journal of Algebra ; 466 (2016). - pp. 195-203. - ISSN 0021-8693. - eISSN 1090-266X |
| ArXiv-ID: | arXiv:1511.01048 |
| DOI (citable link): | https://dx.doi.org/10.1016/j.jalgebra.2016.07.024 |
| Summary: |
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.
|
| Subject (DDC): | 510 Mathematics |
| Keywords: | Real algebra; Number theory; Matrices |
| Comment on publication: | Serious error in previous version |
Cite This
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||
KUMMER, Mario, 2016. Eigenvalues of symmetric matrices over integral domains. In: Journal of Algebra. 466, pp. 195-203. ISSN 0021-8693. eISSN 1090-266X. Available under: doi: 10.1016/j.jalgebra.2016.07.024
@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} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/37288"> <dc:contributor>Kummer, Mario</dc:contributor> <dc:language>eng</dc:language> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:creator>Kummer, Mario</dc:creator> <dcterms:issued>2016</dcterms:issued> <dcterms:title>Eigenvalues of symmetric matrices over integral domains</dcterms:title> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-02-09T14:55:29Z</dcterms:available> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/37288"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-02-09T14:55:29Z</dc:date> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> </rdf:Description> </rdf:RDF>
This item appears in the following Collection(s)
Search KOPS
Browse
My Account
