Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers
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Authors
Yunlan Wei
- School of Mathematics and Statistics, Linyi University, Linyi 276000, China.
- College of Information Technology, The University of Suwon, Hwaseong-si, 445-743, Korea.
Yanpeng Zheng
- School of Automation and Electrical Engineering, Linyi University, Linyi 276000, China.
Zhaolin Jiang
- School of Mathematics and Statistics, Linyi University, Linyi 276000, China.
Sugoog Shon
- College of Information Technology, The University of Suwon, Hwaseong-si, 445-743, Korea.
Abstract
In this paper, we investigate the invertibility of \(n\times n\) skew circulant matrix involving the product of Fibonacci and Lucas numbers, whose determinant and inverse can be expressed by the \((n-1)^{\rm th}\), \(n^{\rm th}\), \((n+1)^{\rm th}\), \((n+2)^{\rm th}\) product of Fibonacci and Lucas numbers. Some norms and bounds for the spread of these matrices are given, respectively. In addition, we generalize these results to skew left circulant matrix involving the product of Fibonacci and Lucas numbers. Finally, several numerical examples are illustrated to show the effectiveness of our theoretical results.
Share and Cite
ISRP Style
Yunlan Wei, Yanpeng Zheng, Zhaolin Jiang, Sugoog Shon, Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers, Journal of Mathematics and Computer Science, 20 (2020), no. 1, 64--78
AMA Style
Wei Yunlan, Zheng Yanpeng, Jiang Zhaolin, Shon Sugoog, Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers. J Math Comput SCI-JM. (2020); 20(1):64--78
Chicago/Turabian Style
Wei, Yunlan, Zheng, Yanpeng, Jiang, Zhaolin, Shon, Sugoog. "Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers." Journal of Mathematics and Computer Science, 20, no. 1 (2020): 64--78
Keywords
- Determinant
- inverse
- norm
- spread
- Fibonacci number
- skew circulant matrix
MSC
- 15A09
- 15A15
- 15B05
- 11B39
- 65F40
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