{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T21:26:55Z","timestamp":1749158815905},"reference-count":7,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.<\/jats:p>","DOI":"10.1515\/spma-2020-0119","type":"journal-article","created":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T22:37:50Z","timestamp":1611355070000},"page":"31-35","source":"Crossref","is-referenced-by-count":1,"title":["Further generalization of symmetric multiplicity theory to the geometric case over a field"],"prefix":"10.1515","volume":"9","author":[{"given":"Isaac","family":"Cinzori","sequence":"first","affiliation":[{"name":"Department of Mathematics , Michigan State University , East Lansing, MI, 48824, USA ."}]},{"given":"Charles R.","family":"Johnson","sequence":"additional","affiliation":[{"name":"Department of Mathematics , College of William and Mary , P.O. Box 8795, Williamsburg, VA 23187-8795, USA ."}]},{"given":"Hannah","family":"Lang","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Harvard University , Cambridge , MA, 02138, USA ."}]},{"given":"Carlos M.","family":"Saiago","sequence":"additional","affiliation":[{"name":"Centro de Matematica e Aplicacoes (CMA\/FCT\/UNL), Departamento de Matematica , Faculdade de Ciencias e Technologia da Universidade NOVA de Lisboa , 2829-516 Quinta da Torre , Portugal ."}]}],"member":"374","published-online":{"date-parts":[[2021,1,19]]},"reference":[{"key":"2021062313143191928_j_spma-2020-0119_ref_001_w2aab3b7b8b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] C.R. Johnson and A. Leal-Duarte. The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree. Linear and Multilinear Algebra 46:139\u2013144 (1999).","DOI":"10.1080\/03081089908818608"},{"key":"2021062313143191928_j_spma-2020-0119_ref_002_w2aab3b7b8b1b6b1ab1ab2Aa","doi-asserted-by":"crossref","unstructured":"[2] C.R. Johnson, A. Leal-Duarte, and C.M. Saiago. The Parter-Wiener theorem: refinement and generalization. SIAM Journal on Matrix Analysis and Applications 25(2):352\u2013361 (2003).","DOI":"10.1137\/S0895479801393320"},{"key":"2021062313143191928_j_spma-2020-0119_ref_003_w2aab3b7b8b1b6b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"[3] C.R. Johnson, A. Leal-Duarte, and C.M. Saiago. Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars. 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Saiago, Eigenvalues, Multiplicities and Graphs, Cambridge University Press, New York, 2018.","DOI":"10.1017\/9781316155158"},{"key":"2021062313143191928_j_spma-2020-0119_ref_007_w2aab3b7b8b1b6b1ab1ab7Aa","doi-asserted-by":"crossref","unstructured":"[7] C.M. Saiago. Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments. Special Matrices 7:316-326 (2019).","DOI":"10.1515\/spma-2019-0025"}],"container-title":["Special Matrices"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/spma\/9\/1\/article-p31.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2020-0119\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2020-0119\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T22:04:05Z","timestamp":1624485845000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2020-0119\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,1]]},"references-count":7,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,29]]},"published-print":{"date-parts":[[2021,1,1]]}},"alternative-id":["10.1515\/spma-2020-0119"],"URL":"https:\/\/doi.org\/10.1515\/spma-2020-0119","relation":{},"ISSN":["2300-7451"],"issn-type":[{"value":"2300-7451","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,1]]}}}