Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers
Circulant type matrices have become an important tool in solving differential equations. In this paper, we consider circulant type matrices, including the circulant and left circulant and g-circulant matrices with the sum and product of Fibonacci and Lucas numbers. Firstly, we discuss the invertibil...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/375251 |
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| _version_ | 1832566765552402432 |
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| author | Zhaolin Jiang Yanpeng Gong Yun Gao |
| author_facet | Zhaolin Jiang Yanpeng Gong Yun Gao |
| author_sort | Zhaolin Jiang |
| collection | DOAJ |
| description | Circulant type matrices have become an important tool in solving differential equations. In this paper, we consider circulant type matrices, including the circulant and left circulant and g-circulant matrices with the sum and product of Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the left circulant and g-circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the left circulant and g-circulant matrices by utilizing the relation between left circulant, and g-circulant matrices and circulant matrix, respectively. |
| format | Article |
| id | doaj-art-7926c0c43ab5465a87654065814a0441 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7926c0c43ab5465a87654065814a04412025-02-03T01:03:12ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/375251375251Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas NumbersZhaolin Jiang0Yanpeng Gong1Yun Gao2Department of Mathematics, Linyi University, Linyi, Shandong 276000, ChinaInstitute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, ChinaInstitute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, ChinaCirculant type matrices have become an important tool in solving differential equations. In this paper, we consider circulant type matrices, including the circulant and left circulant and g-circulant matrices with the sum and product of Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the left circulant and g-circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the left circulant and g-circulant matrices by utilizing the relation between left circulant, and g-circulant matrices and circulant matrix, respectively.http://dx.doi.org/10.1155/2014/375251 |
| spellingShingle | Zhaolin Jiang Yanpeng Gong Yun Gao Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers Abstract and Applied Analysis |
| title | Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers |
| title_full | Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers |
| title_fullStr | Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers |
| title_full_unstemmed | Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers |
| title_short | Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers |
| title_sort | circulant type matrices with the sum and product of fibonacci and lucas numbers |
| url | http://dx.doi.org/10.1155/2014/375251 |
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