{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:31:52Z","timestamp":1760711512428,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T00:00:00Z","timestamp":1754352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shandong Province","award":["ZR2022MA092"],"award-info":[{"award-number":["ZR2022MA092"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper conducts a rigorous study on the spectral properties and operator-space distances of perturbed Dirichlet\u2013Neumann tridiagonal (PDNT) Toeplitz matrices, with emphasis on their asymptotic behaviors. We establish explicit closed-form solutions for the eigenvalues and associated eigenvectors, highlighting their fundamental importance for characterizing matrix stability in the presence of perturbations. By exploiting the structural characteristics of PDNT Toeplitz matrices, we obtain closed-form expressions quantifying the distance to normality, the deviation from normality.<\/jats:p>","DOI":"10.3390\/axioms14080609","type":"journal-article","created":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T13:44:32Z","timestamp":1754401472000},"page":"609","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Structured Distance to Normality of Dirichlet\u2013Neumann Tridiagonal Toeplitz Matrices"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9521-9835","authenticated-orcid":false,"given":"Zhaolin","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Intelligent Science and Control Engineering, Shandong Vocational and Technical University of International Studies, Rizhao 276800, China"},{"name":"School of Mathematics and Statistics, Linyi University, Linyi 276000, China"}]},{"given":"Hongxiao","family":"Chu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Linyi University, Linyi 276000, China"}]},{"given":"Qiaoyun","family":"Miao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"}]},{"given":"Ziwu","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Linyi University, Linyi 276000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1016\/j.laa.2008.09.034","article-title":"Exact eigensystems for some matrices arising from discretizations","volume":"430","author":"Chang","year":"2009","journal-title":"Linear Algebra Its Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"122157","DOI":"10.1016\/j.eswa.2023.122157","article-title":"Explicit potential function and fast algorithm for computing potentials in \u03b1\u00d7\u03b2 conic surface resistor network","volume":"238","author":"Jiang","year":"2024","journal-title":"Expert Syst. 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