{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:04:38Z","timestamp":1760241878710,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501141"],"award-info":[{"award-number":["11501141"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Top-notch Talents Support Project of Education Department of Guizhou Province","award":["QJHKYZ [2016]066"],"award-info":[{"award-number":["QJHKYZ [2016]066"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Firstly, the relationships among strictly diagonally dominant (    S D D    ) matrices, doubly strictly diagonally dominant (    D S D D    ) matrices, eventually     S D D     matrices and eventually     D S D D     matrices are considered. Secondly, by excluding some proper subsets of an existing eigenvalue inclusion set for matrices, which do not contain any eigenvalues of matrices, a tighter eigenvalue inclusion set of matrices is derived. As its application, a sufficient condition of determining non-singularity of matrices is obtained. Finally, the infinity norm estimation of the inverse of eventually     D S D D     matrices is derived.<\/jats:p>","DOI":"10.3390\/sym10100448","type":"journal-article","created":{"date-parts":[[2018,10,2]],"date-time":"2018-10-02T08:23:50Z","timestamp":1538468630000},"page":"448","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Eventually DSDD Matrices and Eigenvalue Localization"],"prefix":"10.3390","volume":"10","author":[{"given":"Caili","family":"Sang","sequence":"first","affiliation":[{"name":"College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, China"},{"name":"School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, Guizhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianxing","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1080\/03081087.2015.1049582","article-title":"An eigenvalue localization set for tensor with applications to determine the positive (semi-)definiteness of tensors","volume":"64","author":"Li","year":"2016","journal-title":"Linear Multilinear Algebra"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sang, C.L., and Li, C.Q. 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Eventually D-SDD, Eventually S-SDD Matrices and the Eigenvalue Inclusion Sets of Matrices, Yunnan University.","DOI":"10.1016\/j.amc.2017.05.011"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Varga, R.S. (2004). Ger\u0161gorin and His Circles, Springer.","DOI":"10.1007\/978-3-642-17798-9"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11075-006-9029-3","article-title":"H-matrix theory vs. eigenvalue localization","volume":"42","year":"2006","journal-title":"Numer. Algorithms"},{"key":"ref_12","unstructured":"Li, S.H., Li, C.Q., and Li, Y.T. (arXiv, 2017). Exclusion sets for eigenvalues of matrices, arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1002\/nla.2028","article-title":"Pseudospectra localizations and their applications","volume":"23","year":"2016","journal-title":"Numer. Linear Algebra Appl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/10\/448\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:23:29Z","timestamp":1760196209000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/10\/448"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,1]]},"references-count":13,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["sym10100448"],"URL":"https:\/\/doi.org\/10.3390\/sym10100448","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,10,1]]}}}