The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers
Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and g-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant ma...
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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/10.1155/2014/931451 |
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| author | Zhaolin Jiang Dan Li |
| author_facet | Zhaolin Jiang Dan Li |
| author_sort | Zhaolin Jiang |
| collection | DOAJ |
| description | Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and g-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant and g-circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant and g-circulant matrices by utilizing the relationship between left circulant, g-circulant matrices and circulant matrix, respectively. |
| format | Article |
| id | doaj-art-0c685674be334ce381ce620837304bc1 |
| 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-0c685674be334ce381ce620837304bc12025-02-03T01:30:53ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/931451931451The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas NumbersZhaolin Jiang0Dan Li1Department of Mathematics, Linyi University, Linyi, Shandong 276000, ChinaDepartment of Mathematics, Linyi University, Linyi, Shandong 276000, ChinaCirculant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and g-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant and g-circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant and g-circulant matrices by utilizing the relationship between left circulant, g-circulant matrices and circulant matrix, respectively.http://dx.doi.org/10.1155/2014/931451 |
| spellingShingle | Zhaolin Jiang Dan Li The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers Abstract and Applied Analysis |
| title | The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers |
| title_full | The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers |
| title_fullStr | The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers |
| title_full_unstemmed | The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers |
| title_short | The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers |
| title_sort | invertibility explicit determinants and inverses of circulant and left circulant and g circulant matrices involving any continuous fibonacci and lucas numbers |
| url | http://dx.doi.org/10.1155/2014/931451 |
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