关于Jacobsthal数和Jacobsthal-Lucas数的r-循环矩阵的行列式和逆
PDF下载 (303)杨 佳,岑建苗 *.关于Jacobsthal数和Jacobsthal-Lucas数的r-循环矩阵的行列式和逆[J].宁波大学学报(理工版),2013,26(02):108-113.DOI:
YANG Jia,CEN Jian-miao *.Determinants and Inverses of r-circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers[J].Journal of Ningbo University(Natural Science & Engineering Edition),2013,26(02):108-113.DOI:
| Title: | Determinants and Inverses of r-circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers |
| 作者: | 杨 佳, 岑建苗 * |
| Author(s): | YANG Jia, CEN Jian-miao * |
| 关键词: | r-循环矩阵; 行列式; 逆; Jacobsthal数; Jacobsthal-Lucas数 |
| Keywords: | r-circulant matrix; determinant; inverse; Jacobsthal number; Jacobsthal-Lucas number |
| 分类号: | O15 |
| 文献标识码: | A |
| 摘要: | 和 是n阶r-循环矩阵, 其中 , 是Jacobsthal数, , 是Jacobsthal-Lucas数, 研究得出了 和 的关于Jacobsthal数和Jacobsthal-Lucas数的行列式的值. 同时, 计算出了矩阵 和 的逆. |
| Abstract: | Let and be r-circulant matrix of order n, where , are the Jacobsthal numbers and , are the Jacobsthal-Lucas numbers. We obtained the values of the determinants of matrices and in terms of the Jacobsthal number and the Jacobsthal-Lucas number. Moreover, the inverses of matrices and are also derived. |
| 参考文献 /References: | [1] Philip J D. Circulant matrices[M]. New York: Wiley Press, 1979. [2] Good I J. On the inversion of circulant matrices[J]. Biometrika, 1950, 37:185-186. [3] Shen Shouqiang, Cen Jianmiao, Yong Hao. On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers[J]. Applied Mathematics and Computation, 2011, 217:9790-9797. [4] Durmus B, Tam T Y. Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers[J]. Applied Mathematics and Computation, 2012, 219:544-551. [5] Frey D D, Sellers J A. Jacobsthal numbers alternating sign matrices[J]. Journal of Integer Sequences, 2000(3): 1-15. |
| 备注/Memo: | Received date: 2012－11－21. Foundation items: Supported by Ningbo Natural Science Foundation (2011A610172). The first author: YANG Jia (1988－), female, Weinan Shaanxi, post of graduate student, research domain: matrix theory. E-mail: yj798859445@163.com *Corresponding author: CEN Jian-miao (1959－), male, Ningbo Zhejiang, professor, research domain: Hopf algebra theory and matrix theory. E-mail: cjmlx@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
