Negafibonacci Numbers via Matrices
In this paper, negafibonacci numbers are generated by means of matrix methods. A 2×2 matrix is used to obtain some properties of negafibonacci numbers; on the other hand, families of tridiagonal matrices are introduced to generate negafibonacci numbers through determinants.
- Autores:
-
Triana Laverde, Juan Gabriel
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2019
- Institución:
- Escuela Colombiana de Ingeniería Julio Garavito
- Repositorio:
- Repositorio Institucional ECI
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.escuelaing.edu.co:001/1390
- Acceso en línea:
- https://repositorio.escuelaing.edu.co/handle/001/1390
- Palabra clave:
- Fibonacci numbers
Matrices
Determinants.
Números de Fibonacci
Matrices
Determinantes
- Rights
- openAccess
- License
- http://purl.org/coar/access_right/c_abf2
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| dc.title.eng.fl_str_mv |
Negafibonacci Numbers via Matrices |
| title |
Negafibonacci Numbers via Matrices |
| spellingShingle |
Negafibonacci Numbers via Matrices Fibonacci numbers Matrices Determinants. Números de Fibonacci Matrices Determinantes |
| title_short |
Negafibonacci Numbers via Matrices |
| title_full |
Negafibonacci Numbers via Matrices |
| title_fullStr |
Negafibonacci Numbers via Matrices |
| title_full_unstemmed |
Negafibonacci Numbers via Matrices |
| title_sort |
Negafibonacci Numbers via Matrices |
| dc.creator.fl_str_mv |
Triana Laverde, Juan Gabriel |
| dc.contributor.author.none.fl_str_mv |
Triana Laverde, Juan Gabriel |
| dc.contributor.researchgroup.spa.fl_str_mv |
Matemáticas |
| dc.subject.proposal.eng.fl_str_mv |
Fibonacci numbers Matrices Determinants. |
| topic |
Fibonacci numbers Matrices Determinants. Números de Fibonacci Matrices Determinantes |
| dc.subject.proposal.spa.fl_str_mv |
Números de Fibonacci Matrices Determinantes |
| description |
In this paper, negafibonacci numbers are generated by means of matrix methods. A 2×2 matrix is used to obtain some properties of negafibonacci numbers; on the other hand, families of tridiagonal matrices are introduced to generate negafibonacci numbers through determinants. |
| publishDate |
2019 |
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2019 2021-05-05T04:26:01Z 2021-10-01T17:20:50Z |
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2019 |
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2021-05-05T04:26:01Z 2021-10-01T17:20:50Z |
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Artículo de revista |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Text |
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1512-0082 |
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https://repositorio.escuelaing.edu.co/handle/001/1390 |
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1512-0082 |
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https://repositorio.escuelaing.edu.co/handle/001/1390 |
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eng |
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eng |
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Vol. 23, No. 1, 2019, 19–24 |
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24 |
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1 |
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19 |
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23 |
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N/A |
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Bulletin of TICMI |
| dc.relation.references.eng.fl_str_mv |
N. Cahill, J. D’errico, N. Narayan, J. Narayan, Fibonacci determinants, College Mathematical Journal, 33, 3 (2002), 221-225 R, Dunlap, The Golden Ratio and Fibonacci Numbers, World scientific, Singapore, 1997 H. Gulec, N. Taskara, K. Uslu, A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Applied Mathematics and Computation, 220 (2013), 482-486 C. King, Some Properties of Fibonacci Numbers, San Jose State College: Master’s Thesis, 1960 P. Trojovsky, On a sequence of tridiagonal matrices whose determinants are fibonacci numbers Fn+1, International Journal of Pure and Applied Mathematics, 102, 3 (2015), 527-532 I. Matousova, P. Trojovsky, On a sequence of tridiagonal matrices whose permanents are related to Fibonacci and Lucas numbers, International Journal of Pure and Applied Mathematics, 105, 4 (2015), 715721 T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & sons, New York, 2001 A, Posamentier, I. Lehmann, The Fabulous Fibonacci Numbers, Prometheus Books, New York, 2007 H. Belbachir, S. Laszlo, Fibonacci and Lucas Pascal triangles, Hacettepe journal of mathematics and statistics, 45, 5 (2016), 1343-1354 R. Keskin, B. Demirturk, Some new Fibonacci and Lucas identities by matrix methods, International Journal of Mathematical Education in Science and Technology, 41, 3 (2010), 379-387 G. Strang, Linear Algebra and its Applications, Thomson Brooks/Cole, Belmont, 2006 N. Voll, The Cassini identity and its relative, Fibonacci Quarterly, 48, 3 (2010), 197-201 |
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openAccess |
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http://purl.org/coar/access_right/c_abf2 |
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6 páginas |
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application/pdf |
| dc.publisher.eng.fl_str_mv |
Universidad Estatal de Tbilisi |
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Georgia |
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https://www.emis.de/journals/TICMI/vol23_1/3_triana.pdf |
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Escuela Colombiana de Ingeniería Julio Garavito |
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Triana Laverde, Juan Gabriel244558d50c4189ca5db2880ea0a000bb600Matemáticas2021-05-05T04:26:01Z2021-10-01T17:20:50Z20192021-05-05T04:26:01Z2021-10-01T17:20:50Z20191512-0082https://repositorio.escuelaing.edu.co/handle/001/1390In this paper, negafibonacci numbers are generated by means of matrix methods. A 2×2 matrix is used to obtain some properties of negafibonacci numbers; on the other hand, families of tridiagonal matrices are introduced to generate negafibonacci numbers through determinants.En este trabajo, los números negafibonacci se generan mediante métodos matriciales. Una matriz de 2×2 se utiliza para obtener algunas propiedades de los números negafibonacci; por otra parte, se introducen familias de matrices tridiagonales para generar números negafibonacci mediante determinantes.Universidad Nacional de Colombia, Bogot´a, Colombia (Received November 01, 2018; Revised June 08, 2019; Accepted June 24, 2019)6 páginasapplication/pdfengUniversidad Estatal de TbilisiGeorgiahttps://www.emis.de/journals/TICMI/vol23_1/3_triana.pdfNegafibonacci Numbers via MatricesArtículo de revistainfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85Vol. 23, No. 1, 2019, 19–242411923N/ABulletin of TICMIN. Cahill, J. D’errico, N. Narayan, J. Narayan, Fibonacci determinants, College Mathematical Journal, 33, 3 (2002), 221-225R, Dunlap, The Golden Ratio and Fibonacci Numbers, World scientific, Singapore, 1997H. Gulec, N. Taskara, K. Uslu, A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Applied Mathematics and Computation, 220 (2013), 482-486C. King, Some Properties of Fibonacci Numbers, San Jose State College: Master’s Thesis, 1960P. Trojovsky, On a sequence of tridiagonal matrices whose determinants are fibonacci numbers Fn+1, International Journal of Pure and Applied Mathematics, 102, 3 (2015), 527-532I. Matousova, P. Trojovsky, On a sequence of tridiagonal matrices whose permanents are related to Fibonacci and Lucas numbers, International Journal of Pure and Applied Mathematics, 105, 4 (2015), 715721T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & sons, New York, 2001A, Posamentier, I. Lehmann, The Fabulous Fibonacci Numbers, Prometheus Books, New York, 2007H. Belbachir, S. Laszlo, Fibonacci and Lucas Pascal triangles, Hacettepe journal of mathematics and statistics, 45, 5 (2016), 1343-1354R. Keskin, B. Demirturk, Some new Fibonacci and Lucas identities by matrix methods, International Journal of Mathematical Education in Science and Technology, 41, 3 (2010), 379-387G. Strang, Linear Algebra and its Applications, Thomson Brooks/Cole, Belmont, 2006N. Voll, The Cassini identity and its relative, Fibonacci Quarterly, 48, 3 (2010), 197-201info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Fibonacci numbersMatricesDeterminants.Números de FibonacciMatricesDeterminantesLICENSElicense.txttext/plain1881https://repositorio.escuelaing.edu.co/bitstream/001/1390/1/license.txt5a7ca94c2e5326ee169f979d71d0f06eMD51open accessORIGINALNegafibonacci Numbers via Matrices.pdfapplication/pdf102081https://repositorio.escuelaing.edu.co/bitstream/001/1390/2/Negafibonacci%20Numbers%20via%20Matrices.pdf36e23e9aa1f6568484ec70cc370881edMD52open accessTEXTNegafibonacci Numbers via Matrices.pdf.txtNegafibonacci Numbers via Matrices.pdf.txtExtracted texttext/plain9514https://repositorio.escuelaing.edu.co/bitstream/001/1390/3/Negafibonacci%20Numbers%20via%20Matrices.pdf.txt08d45c80d1d982d38e00890433b7f19cMD53open accessTHUMBNAILNegafibonacci Numbers via Matrices.pdf.jpgNegafibonacci Numbers via Matrices.pdf.jpgGenerated Thumbnailimage/jpeg8271https://repositorio.escuelaing.edu.co/bitstream/001/1390/4/Negafibonacci%20Numbers%20via%20Matrices.pdf.jpg4793d17e06b1bd7241bce0ae85e6df26MD54open access001/1390oai:repositorio.escuelaing.edu.co:001/13902021-10-01 18:02:18.48open accessRepositorio Escuela Colombiana de Ingeniería Julio Garavitorepositorio.eci@escuelaing.edu.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 |