{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:07:26Z","timestamp":1760242046594,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,12]],"date-time":"2018-12-12T00:00:00Z","timestamp":1544572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Outstanding Youth Cultivation Project for Yunnan Province","award":["2018YDJQ021"],"award-info":[{"award-number":["2018YDJQ021"]}]},{"name":"Applied Basic Research Programs of Science and Technology 61 Department of Yunnan Province","award":["2018FB001"],"award-info":[{"award-number":["2018FB001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A set to locate all eigenvalues for matrices with a constant main diagonal entry is given, and it is proved that this set is tighter than the well-known Ger\u0161gorin set, the Brauer set and the set proposed in (Linear and Multilinear Algebra, 60:189-199, 2012). Furthermore, by applying this result to Toeplitz matrices as a subclass of matrices with a constant main diagonal, we obtain a set including all eigenvalues of Toeplitz matrices.<\/jats:p>","DOI":"10.3390\/sym10120745","type":"journal-article","created":{"date-parts":[[2018,12,12]],"date-time":"2018-12-12T10:54:26Z","timestamp":1544612066000},"page":"745","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Eigenvalue Inclusion Set for Matrices with a Constant Main Diagonal Entry"],"prefix":"10.3390","volume":"10","author":[{"given":"Weiqian","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466399, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoqian","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1215\/S0012-7094-47-01403-8","article-title":"Limits for the characteristic roots of a matrix II","volume":"14","author":"Brauer","year":"1947","journal-title":"Duke Math. 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[2nd ed.]."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/12\/745\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:33:37Z","timestamp":1760196817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/12\/745"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,12]]},"references-count":19,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["sym10120745"],"URL":"https:\/\/doi.org\/10.3390\/sym10120745","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,12,12]]}}}