Explicit formulae for spectral norms of circulant-type matrices with some given entries

TL;DR

This paper derives explicit formulas for the spectral norms of circulant matrices with entries based on Fibonacci and Lucas numbers, providing theoretical insights and numerical verification.

Contribution

It introduces explicit spectral norm formulas for circulant matrices with Fibonacci and Lucas entries, advancing understanding of their spectral properties.

Findings

Derived explicit spectral norm formulas for specific circulant matrices.

Provided numerical tests confirming theoretical results.

Enhanced analytical tools for matrices with Fibonacci and Lucas entries.

Abstract

In this paper we investigate the spectral norm for circulant matrices, whose entries are modified Fibonacci numbers and Lucas numbers. We obtain the identity estimations for the spectral norms. Some numerical test results are listed to verify the results using those approaches.