On the spectral norms of some special $g$-circulant matrices

Year 2016, Volume: 45 Issue: 5, 1441 - 1448, 01.10.2016

Shou-qiang Shen Wei-jun Liu Jun-jie He

Abstract

In the present paper, we give upper and lower bounds for the spectral norm of $g$-circulant matrix, whose the first row entries are the classical Horadam numbers $U_i^{(a,b)}$. In addition, we also establish an explicit formula of the spectral norm for $g$-circulant matrix with the first row $([U_0^{(a,b)}]^2,[U_1^{(a,b)}]^2, \cdot, [U_{n-1}^{(a,b)}]^2)$.

Keywords

$g$-Circulant matrix , Spectral norm , Horadam number , Fibonacci number , Lucas number

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