Mathematical Theory and Applications ›› 2018, Vol. 38 ›› Issue (3-4): 59-68.

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On the Norms of r-circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers

He Chengyuan, Qiu Tao,  Lei Lin   

  • Online:2018-12-30 Published:2020-09-21

Abstract: In this paper we study the norms of r-circulant matricesA = Cr(J0,J1, …,Jn-1) and B =Cr(D0,D1,…,Dn-1)where Jnand Dnare Jacobsthal and Jacobsthal-Lucas numbers,and give some boundsfor the spectral norms of Kronecker and Hadamard products ofthe r-matrices Aand B. 

Key words: Jacobsthal number, Jacobsthal-Lucas number, R-circulant matrix, Euclidean norm , Spectral norm