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

Authors : Shou-qiang SHEN, Wei-jun LİU, Jun-jie HE

Pages : 1441-1448

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Publication Date : 2016-10-01

Article Type : Research Paper

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 $U_i^{insert ignore into journalissuearticles values(a,b);}$. In addition, we also establish an explicit formula of the spectral norm for $g$-circulant matrix with the first row $insert ignore into journalissuearticles values([U_0^{insert ignore into journalissuearticles values(a,b);}]^2,[U_1^{insert ignore into journalissuearticles values(a,b);}]^2, \cdot, [U_{n-1}^{insert ignore into journalissuearticles values(a,b);}]^2);$.
Keywords : g Circulant matrix, Spectral norm, Horadam number, Fibonacci number, Lucas number