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.

引用

页码：522 / 535

页数：14

共 41 条

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[40] On the Norms and Eigenvalues of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r$$\end{document}-Circulant Matrices with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-Mersenne and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-Mersenne–Lucas Numbers
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Mathematical Notes, 2023, 114 (3-4) : 522 - 535

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