Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix
In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the exp...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-08-01
|
| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2021-0145 |
| _version_ | 1811222919345340416 |
|---|---|
| author | Jiang Zhaolin Zheng Yanpeng Li Tianzi |
| author_facet | Jiang Zhaolin Zheng Yanpeng Li Tianzi |
| author_sort | Jiang Zhaolin |
| collection | DOAJ |
| description | In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the explicit formulas for its determinant and inverse. |
| first_indexed | 2024-04-12T08:24:22Z |
| format | Article |
| id | doaj.art-601cc38777e7426693b53bebd625f150 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-04-12T08:24:22Z |
| publishDate | 2021-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-601cc38777e7426693b53bebd625f1502022-12-22T03:40:28ZengDe GruyterSpecial Matrices2300-74512021-08-01101404610.1515/spma-2021-0145Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrixJiang Zhaolin0Zheng Yanpeng1Li Tianzi2School of Mathematics and Statistics, Linyi University, Linyi276000, ChinaSchool of Automation and Electrical Engineering, Linyi University, Linyi276000, ChinaSchool of Mathematics and Statistics, Linyi University, Linyi276000, ChinaIn this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the explicit formulas for its determinant and inverse.https://doi.org/10.1515/spma-2021-0145sylvester-kac matrixfibonacci numbercharacteristic polynomialdeterminantinverse15a0915a1515a18 |
| spellingShingle | Jiang Zhaolin Zheng Yanpeng Li Tianzi Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix Special Matrices sylvester-kac matrix fibonacci number characteristic polynomial determinant inverse 15a09 15a15 15a18 |
| title | Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix |
| title_full | Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix |
| title_fullStr | Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix |
| title_full_unstemmed | Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix |
| title_short | Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix |
| title_sort | characteristic polynomial determinant and inverse of a fibonacci sylvester kac matrix |
| topic | sylvester-kac matrix fibonacci number characteristic polynomial determinant inverse 15a09 15a15 15a18 |
| url | https://doi.org/10.1515/spma-2021-0145 |
| work_keys_str_mv | AT jiangzhaolin characteristicpolynomialdeterminantandinverseofafibonaccisylvesterkacmatrix AT zhengyanpeng characteristicpolynomialdeterminantandinverseofafibonaccisylvesterkacmatrix AT litianzi characteristicpolynomialdeterminantandinverseofafibonaccisylvesterkacmatrix |