The Representations of the Fibonacci and Lucas Matrices
| dc.contributor.author | Koken, Fikri | |
| dc.date.accessioned | 2024-02-23T14:00:11Z | |
| dc.date.available | 2024-02-23T14:00:11Z | |
| dc.date.issued | 2019 | |
| dc.department | NEÜ | en_US |
| dc.description.abstract | In this study, a matrix R-L is defined by the properties associated with the Pascal matrix, and two closed- form expressions of the matrix function f (R-L) = R-L(n) are determined by methods in matrix theory. These expressions satisfy a connection between the integer sequences of the first-second kinds and the Pascal matrices. The matrix R-L(n) is the Fibonacci Lucas matrix, whose entries are the Fibonacci and Lucas numbers. Also, the representations of the Lucas matrix are derived by the matrix function f (R-L - 5I), and various forms of the matrix (R-L - 5I)(n) in terms of a binomial coefficient are studied by methods in number theory. These representations give varied ways to obtain the new Fibonacci- and Lucas- type identities via several properties of the matrices R-L(n) and (R-L - 5I)(n). | en_US |
| dc.identifier.doi | 10.1007/s40995-019-00715-3 | |
| dc.identifier.endpage | 2448 | en_US |
| dc.identifier.issn | 1028-6276 | |
| dc.identifier.issn | 2364-1819 | |
| dc.identifier.issue | A5 | en_US |
| dc.identifier.scopus | 2-s2.0-85073235296 | en_US |
| dc.identifier.scopusquality | Q2 | en_US |
| dc.identifier.startpage | 2443 | en_US |
| dc.identifier.uri | https://doi.org/10.1007/s40995-019-00715-3 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12452/11496 | |
| dc.identifier.volume | 43 | en_US |
| dc.identifier.wos | WOS:000487075500041 | en_US |
| dc.identifier.wosquality | Q3 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Springer International Publishing Ag | en_US |
| dc.relation.ispartof | Iranian Journal Of Science And Technology Transaction A-Science | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Fibonacci Number | en_US |
| dc.subject | Lucas Number | en_US |
| dc.subject | Fibonacci Matrix | en_US |
| dc.subject | Lucas Matrix | en_US |
| dc.subject | Pascal Matrix | en_US |
| dc.title | The Representations of the Fibonacci and Lucas Matrices | en_US |
| dc.type | Article | en_US |
