Algebraic properties of generalized Fibonacci Sequence via matrix Methods
Over the past centuries, the fascination over the Fibonacci sequences and their generalizations has been shown by mathematicians and the wider scientific community. While most of the known algebraic properties of these sequences were found based on the well-known Binet formula, new discoveries seeme...
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| Format: | Article |
| Language: | English |
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Medwell Journals
2016
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| Online Access: | http://eprints.sunway.edu.my/592/ http://eprints.sunway.edu.my/592/1/Sia%20Jye%20Ying%20Algebraic%20Properties%20of%20Generalized%20Fibonacci%20Sequence.pdf |
| _version_ | 1848801855529811968 |
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| author | Sia, Jye Ying* Ho, Chee-Kit * Haslinda Ibrahim, Nazihah Ahmad, |
| author_facet | Sia, Jye Ying* Ho, Chee-Kit * Haslinda Ibrahim, Nazihah Ahmad, |
| author_sort | Sia, Jye Ying* |
| building | SU Institutional Repository |
| collection | Online Access |
| description | Over the past centuries, the fascination over the Fibonacci sequences and their generalizations has been shown by mathematicians and the wider scientific community. While most of the known algebraic properties of these sequences were found based on the well-known Binet formula, new discoveries seemed to have been dwarfed by the nature of the complexity of its methodology. Recently, matrix method has become a popular tool among many researchers working on Fibonacci related sequences. In this study, we investigate the generalized Fibonacci sequence by employing two different matrix methods, namely, the method of diagonalization and the method of matrix collation, making use of several generating matrices. We obtained some new algebraic properties and the sum of the generalized fibonacci sequence with different indices |
| first_indexed | 2025-11-14T21:14:05Z |
| format | Article |
| id | sunway-592 |
| institution | Sunway University |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T21:14:05Z |
| publishDate | 2016 |
| publisher | Medwell Journals |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | sunway-5922019-07-04T08:06:06Z http://eprints.sunway.edu.my/592/ Algebraic properties of generalized Fibonacci Sequence via matrix Methods Sia, Jye Ying* Ho, Chee-Kit * Haslinda Ibrahim, Nazihah Ahmad, QA Mathematics Over the past centuries, the fascination over the Fibonacci sequences and their generalizations has been shown by mathematicians and the wider scientific community. While most of the known algebraic properties of these sequences were found based on the well-known Binet formula, new discoveries seemed to have been dwarfed by the nature of the complexity of its methodology. Recently, matrix method has become a popular tool among many researchers working on Fibonacci related sequences. In this study, we investigate the generalized Fibonacci sequence by employing two different matrix methods, namely, the method of diagonalization and the method of matrix collation, making use of several generating matrices. We obtained some new algebraic properties and the sum of the generalized fibonacci sequence with different indices Medwell Journals 2016 Article PeerReviewed text en http://eprints.sunway.edu.my/592/1/Sia%20Jye%20Ying%20Algebraic%20Properties%20of%20Generalized%20Fibonacci%20Sequence.pdf Sia, Jye Ying* and Ho, Chee-Kit * and Haslinda Ibrahim, and Nazihah Ahmad, (2016) Algebraic properties of generalized Fibonacci Sequence via matrix Methods. Journal of Engineering & Applied Sciences, 11 (11). pp. 2396-2401. ISSN 1816-949X http://medwelljournals.com/abstract/?doi=jeasci.2016.2396.2401 10.3923/jeasci.2016.2396.2401 |
| spellingShingle | QA Mathematics Sia, Jye Ying* Ho, Chee-Kit * Haslinda Ibrahim, Nazihah Ahmad, Algebraic properties of generalized Fibonacci Sequence via matrix Methods |
| title | Algebraic properties of generalized Fibonacci Sequence via matrix Methods |
| title_full | Algebraic properties of generalized Fibonacci Sequence via matrix Methods |
| title_fullStr | Algebraic properties of generalized Fibonacci Sequence via matrix Methods |
| title_full_unstemmed | Algebraic properties of generalized Fibonacci Sequence via matrix Methods |
| title_short | Algebraic properties of generalized Fibonacci Sequence via matrix Methods |
| title_sort | algebraic properties of generalized fibonacci sequence via matrix methods |
| topic | QA Mathematics |
| url | http://eprints.sunway.edu.my/592/ http://eprints.sunway.edu.my/592/ http://eprints.sunway.edu.my/592/ http://eprints.sunway.edu.my/592/1/Sia%20Jye%20Ying%20Algebraic%20Properties%20of%20Generalized%20Fibonacci%20Sequence.pdf |