# Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers

Volume 20, Issue 1, pp 64--78
Publication Date: September 24, 2019 Submission Date: July 30, 2019 Revision Date: August 06, 2019 Accteptance Date: August 27, 2019
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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.

### Keywords

• Determinant
• inverse
• norm
• Fibonacci number
• skew circulant matrix

•  15A09
•  15A15
•  15B05
•  11B39
•  65F40

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