A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers
We use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expres...
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| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4782594 |
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| author | Jiangming Ma Tao Qiu Chengyuan He |
| author_facet | Jiangming Ma Tao Qiu Chengyuan He |
| author_sort | Jiangming Ma |
| collection | DOAJ |
| description | We use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time. |
| format | Article |
| id | doaj-art-81d056a53b2744cabcbd3cc20ee534de |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
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| series | Journal of Mathematics |
| spelling | doaj-art-81d056a53b2744cabcbd3cc20ee534de2025-08-20T02:09:06ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/4782594A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas NumbersJiangming Ma0Tao Qiu1Chengyuan He2School of EconomicsSichuan Deyang No. 5 Middle SchoolSchool of ScienceWe use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time.http://dx.doi.org/10.1155/2021/4782594 |
| spellingShingle | Jiangming Ma Tao Qiu Chengyuan He A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers Journal of Mathematics |
| title | A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers |
| title_full | A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers |
| title_fullStr | A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers |
| title_full_unstemmed | A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers |
| title_short | A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers |
| title_sort | new method of matrix decomposition to get the determinants and inverses of r circulant matrices with fibonacci and lucas numbers |
| url | http://dx.doi.org/10.1155/2021/4782594 |
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