{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T15:12:26Z","timestamp":1774797146957,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,31]],"date-time":"2022-07-31T00:00:00Z","timestamp":1659225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let A be a diagonalizable complex matrix. In this paper, we discuss finding solutions to the Yang\u2013Baxter-like matrix equation AXA=XAX. We then present a concrete example to illustrate the validity of the results obtained.<\/jats:p>","DOI":"10.3390\/sym14081577","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T23:49:27Z","timestamp":1659397767000},"page":"1577","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Finding Solutions to the Yang\u2013Baxter-like Matrix Equation for Diagonalizable Coefficient Matrix"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8838-8702","authenticated-orcid":false,"given":"Dongmei","family":"Chen","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China"}]},{"given":"Xuerong","family":"Yong","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, The University of Puerto Rico Mayaguez, Mayag\u00fce, PR 00681, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.aml.2018.02.017","article-title":"Solving a class of quadratic matrix equations","volume":"82","author":"Adam","year":"2018","journal-title":"Appl. Math. Lett."},{"key":"ref_2","first-page":"1022","article-title":"All Solutions of the Yang-Baxter-like matrix equation when A3=A","volume":"9","author":"Adam","year":"2019","journal-title":"J. Appl. Anal. Comput."},{"key":"ref_3","unstructured":"Cibotarica, A. (2011). An Examination of the Yang-Baxter Equation. [Master\u2019s Thesis, The University of Southern Mississippi]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"347","DOI":"10.3934\/naco.2013.3.347","article-title":"Solutions of the Yang-Baxter matrix equation for an idempotent. Numer","volume":"3","author":"Cibotarica","year":"2013","journal-title":"Algebra Control Optim."},{"key":"ref_5","first-page":"523","article-title":"Explicit solutions of the Yang-Baxter-like matrix equation for a diagonalizable matrix with spectrum {1,\u03b1,0}","volume":"348","author":"Chen","year":"2019","journal-title":"Appl. Math. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"277","DOI":"10.4208\/eajam.150512.231012a","article-title":"A nontrivial solution to a stochastic matrix equation","volume":"2","author":"Ding","year":"2012","journal-title":"East Asian J. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.jmaa.2013.01.054","article-title":"Spectral solutions of the Yang-Baxter matrix equation","volume":"402","author":"Ding","year":"2013","journal-title":"J. Math. Anal. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"352","DOI":"10.4208\/eajam.130713.221113a","article-title":"Further solutions of a Yang-Baxter-like matrix equation","volume":"2","author":"Ding","year":"2013","journal-title":"East Asian J. Appl. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.aml.2013.11.007","article-title":"On the structure of the spectral solutions of the Yang-Baxter matrix equation","volume":"35","author":"Ding","year":"2014","journal-title":"Appl. Math. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.aml.2014.11.017","article-title":"Commuting solutions of the Yang-Baxter matrix equation","volume":"44","author":"Ding","year":"2015","journal-title":"Appl. Math. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1016\/j.camwa.2016.07.015","article-title":"Solving the Yang-Baxter-like matrix equation for a class of elementary matrices","volume":"72","author":"Ding","year":"2016","journal-title":"Comput. Math. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.camwa.2016.04.047","article-title":"Complete commuting solutions of the Yang-Baxter-like matrix equation for diagonalizable matrices","volume":"72","author":"Dong","year":"2016","journal-title":"Comput. Math. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1142\/S1005386718000032","article-title":"Commuting solutions of a quadratic matrix equation for nilpotent matrices","volume":"25","author":"Dong","year":"2018","journal-title":"Algebra. Colloq."},{"key":"ref_14","first-page":"246","article-title":"Iterative methods for finding commuting solutions of the Yang-Baxter-like matrix equation","volume":"333","author":"Kumar","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s00009-022-01982-y","article-title":"Explicit solutions of the singular Yang-Baxter-like matrix equation and their numerical computation","volume":"19","author":"Kumar","year":"2022","journal-title":"Mediterr. J. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.aml.2016.07.021","article-title":"Explicit solutions of the Yang-Baxter-like matrix equation for an idempotent matrix","volume":"63","author":"Mansour","year":"2017","journal-title":"Appl. Math. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1016\/j.camwa.2018.05.042","article-title":"Commuting solutions of the Yang-Baxter-like matrix equation for a class of rank-two updated matrices","volume":"76","author":"Ren","year":"2018","journal-title":"Comput. Math. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/j.jmaa.2018.02.030","article-title":"On commuting solutions of the Yang-Baxter-like matrix equation","volume":"462","author":"Shen","year":"2018","journal-title":"J. Math. Anal. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"106048","DOI":"10.1016\/j.aml.2019.106048","article-title":"All solutions of the Yang-Baxter-like matrix equation for diagonalizable coefficient matrix with two different eigenvalues","volume":"101","author":"Shen","year":"2020","journal-title":"Appl. Math. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.aml.2015.07.009","article-title":"All solutions of the Yang-Baxter-like matrix equation for rank-one matrices","volume":"51","author":"Tian","year":"2016","journal-title":"Appl. Math. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1103\/PhysRevLett.19.1312","article-title":"Some exact results for the many-body problem in one dimension with repulsive delta-function interaction","volume":"19","author":"Yang","year":"1967","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.cam.2016.09.007","article-title":"Solving the Yang-Baxter-like matrix equation for rank-two matrices","volume":"313","author":"Zhou","year":"2017","journal-title":"J. Comput. Appl. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0003-4916(72)90335-1","article-title":"Partition function of the eight-vertex lattice model","volume":"70","author":"Baxter","year":"1972","journal-title":"Ann. Phys."},{"key":"ref_24","unstructured":"Horn, R., and Johnson, C. (1991). Matrix Analysis, Cambridge University Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1577\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:00:19Z","timestamp":1760140819000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,31]]},"references-count":24,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["sym14081577"],"URL":"https:\/\/doi.org\/10.3390\/sym14081577","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,31]]}}}