On the Norms and Eigenvalues of r-Circulant Matrices with k-Mersenne and k-Mersenne-Lucas Numbers

被引：0
|
作者：
Kumari, Munesh [1 ]
Prasad, Kalika [1 ]
Ozkan, Engin [2 ]
Tanti, Jagmohan [3 ]
机构：
[1] Cent Univ Jharkhand, Dept Math, Ranchi 835205, India
[2] Erzincan Binali Yildirim Univ, Dept Math, Erzincan, Turkiye
[3] Babasaheb Bhimrao Ambedkar Univ, Dept Math, Lucknow 226025, India
来源：
MATHEMATICAL NOTES | 2023年 / 114卷 / 3-4期
关键词：
k-Mersenne number; k-Mersenne-Lucas number; r-circulant matrix; eigenvalue; Euclidean norm; spectral norm; FIBONACCI;
D O I：
10.1134/S0001434623090225
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
this work, we study the r-circulant matrix C-r = Circ(r)(c(0), c(1), c(2), ..., c(n-1)) such that the entries of C-r are c(i) = M(k,a+ib )or ci = R-k,R-a+ib, where M-k,M-a+ib and R-k,R-a+ib are k-Mersenne and k-Mersenne-Lucas numbers, respectively. We obtain the eigenvalues and determinants for the matrices and some important identities for the k-Mersenne and k-Mersenne-Lucas numbers. Furthermore, we find norms and bounds estimation for the spectral norm for these r-circulant matrices.
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页码：522 / 535
页数：14
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