# Improved Bounds for the Spectral Norms of $r$-circulant Matrices with $k$-fibonacci and $k$-lucasnumbers

Volume 12, Issue 1, pp 39-50
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### Authors

Lele Liu - College of Science, University of Shanghai for Science and Technology,Shanghai 200093, China.

### Abstract

We are concerned with the spectral norms of $r$-circulant matrices with the $k$-Fibonacci and $k$-Lucas numbers. By using Abel transformation and some identities, weobtain some new lower bounds for the spectral norms of $r$-circulant matrices. Havingcompared some known results, the obtained bounds are more precise.

### Keywords

• $k$-Fibonacci number
• $k$-Lucas number
• $r$-circulant matrix
• Spectral norm.

•  11B39
•  11C20
•  15A45

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