{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T16:15:21Z","timestamp":1765901721723,"version":"3.48.0"},"reference-count":17,"publisher":"Centre for Evaluation in Education and Science (CEON\/CEES)","issue":"2","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/BY-SA\/4.0"}],"funder":[{"name":"The first three authors thank the Portuguese funds through FCT - Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, within the project UID\/00013, Research Centre CMAT-UTAD"},{"name":"The fourth author expresses her sincere thanks to the Federal University of Mato Grosso do Sul - UFMS\/MEC - Brazil for their valuable support"},{"name":"The last author was partially supported by PROPESQ-UFT"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematica Moravica"],"published-print":{"date-parts":[[2025]]},"abstract":"<jats:p>In this study, we consider the Toeplitz matrices with entries being Leonardo numbers. We have found upper and lower bounds for the spectral norms of these matrices, considering also the Hadamard product of this type of matrix.<\/jats:p>","DOI":"10.5937\/matmor2502049c","type":"journal-article","created":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T15:59:06Z","timestamp":1765900746000},"page":"49-66","source":"Crossref","is-referenced-by-count":0,"title":["On the norms and Hadamard product of Toeplitz matrices involving Leonardo numbers"],"prefix":"10.5937","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6917-5093","authenticated-orcid":false,"given":"Paula","family":"Catarino","sequence":"first","affiliation":[{"name":"University of Tr\u00e1s-os-Montes and Alto Douro, Department of Mathematics, Vila Real, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6166-8245","authenticated-orcid":false,"given":"Anabela","family":"Borges","sequence":"additional","affiliation":[{"name":"University of Tr\u00e1s-os-Montes and Alto Douro, Department of Mathematics, Vila Real, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5460-4297","authenticated-orcid":false,"given":"Paulo","family":"Vasco","sequence":"additional","affiliation":[{"name":"University of Tr\u00e1s-os-Montes and Alto Douro, Department of Mathematics, Vila Real, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6079-2458","authenticated-orcid":false,"given":"Elen","family":"Spreafico","sequence":"additional","affiliation":[{"name":"Federal University of Mato Grosso do Sul, Institute of Mathematics, Campo Grande, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6684-9961","authenticated-orcid":false,"given":"Eudes","family":"Costa","sequence":"additional","affiliation":[{"name":"Federal University of Tocantins, Department of Mathematics, Arraias, Brazil"}]}],"member":"3964","reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"A. Altassan, M. Alan, Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers, Mathematica Slovaca, 74 (3) (2024), 563-576;","DOI":"10.1515\/ms-2024-0042"},{"key":"ref2","unstructured":"M. Akbulak, D. Bozkurt, On the norms of Toeplitz matrices involving Fibonacci and Lucas numbers, Hacettepe Journal of Mathematics and Statistics, 37 (2) (2008), 89-95;"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"U.Bednarz, M.Wo\u0142owiec-Musia\u0142, Generalized Fibonacci-Leonardo numbers, Journal of Difference Equations and Applications, 30v(1) (2024), 111-122;","DOI":"10.1080\/10236198.2023.2265509"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"P. D. Beites, P. Catarino, On the Leonardo quaternions sequence, Hacettepe Journal of Mathematics and Statistics, 53 (4) (2024), 1001-1023;","DOI":"10.15672\/hujms.1197693"},{"key":"ref5","doi-asserted-by":"crossref","unstructured":"H. Bensella, D. Behloul, Common terms of Leonardo and Jacobsthal numbers, Rendiconti del Circolo Matematico di Palermo Series 2, 73 (2024), 259-265;","DOI":"10.1007\/s12215-023-00920-5"},{"key":"ref6","unstructured":"P. Catarino, A. Borges, On Leonardo numbers, Acta Mathematica Universitatis Comenianae, 89 (1) (2020), 75-86;"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"S. Falcon, On the Extended (k,t)-Fibonacci Numbers, Journal of Advances in Mathematics and Computer Science, 39 (7) (2024), 81-89;","DOI":"10.9734\/jamcs\/2024\/v39i71914"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2001;","DOI":"10.1002\/9781118033067"},{"key":"ref9","unstructured":"T. Goy, M. Shattuck, Fibonacci and Lucas identities from Toeplitz-Hessenberg matrices, Applications and Applied Mathematics: An International Journal (AAM), 14 (2) (2019), 699-715;"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"T. Goy, M. Shattuck, Determinants of Toeplitz-Hessenberg matrices with generalized Fibonacci entries, Notes on Number Theory and Discrete Mathematics, 25(4)(2019), 83-95;","DOI":"10.7546\/nntdm.2019.25.4.83-95"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"R. Mathias, The spectral norm of a nonnegative matrix, Linear Algebra and its Applications, 139 (1990), 269-284;","DOI":"10.1016\/0024-3795(90)90403-Y"},{"key":"ref12","doi-asserted-by":"crossref","unstructured":"C. D. Meyer, Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics (SIAM), 2000;","DOI":"10.1137\/1.9780898719512"},{"key":"ref13","unstructured":"B. Prasad, A new Gaussian Fibonacci matrices and its applications, Journal of Algebra and Related Topics, 7 (1) (2019), 65-72;"},{"key":"ref14","doi-asserted-by":"crossref","unstructured":"R. Reams, Hadamard inverses, square roots and products of almost semidefinite matrices, Linear Algebra and its Applications, 288, 35-43, 1999;","DOI":"10.1016\/S0024-3795(98)10162-3"},{"key":"ref15","unstructured":"S. Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory and Applications, Ellis Horwood Ltd., 1989;"},{"key":"ref16","doi-asserted-by":"crossref","unstructured":"R.P.M. Vieira, M.C.S. Mangueira, F.R.V. Alves, P.M.M.C. Catarino, A forma matricial dos n\u00fameros de Leonardo, Ciencia e Natura, 42 (1) (e100) (2020), 1-6;","DOI":"10.5902\/2179460X41839"},{"key":"ref17","doi-asserted-by":"crossref","unstructured":"G. Zielke, Some remarks on matrix norms, condition numbers, and error estimates for linear equations, Linear Algebra and its Applications, 110 (1988), 29-41;","DOI":"10.1016\/0024-3795(83)90130-1"}],"container-title":["Mathematica Moravica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/scindeks-clanci.ceon.rs\/data\/pdf\/1450-5932\/2025\/1450-59322502049C.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T15:59:25Z","timestamp":1765900765000},"score":1,"resource":{"primary":{"URL":"https:\/\/scindeks.ceon.rs\/Article.aspx?artid=1450-59322502049C"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.5937\/matmor2502049c","relation":{},"ISSN":["1450-5932","2560-5542"],"issn-type":[{"value":"1450-5932","type":"print"},{"value":"2560-5542","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]}}}