On k-Circulant matrices involving the Lucas numbers of even index
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Biljana Radičić
Abstract
Let k be a nonzero complex number. In this paper, we consider a k-circulant matrix whose first row is (L2, L4, … , L2n), where Ln is the nth Lucas number. The formulae for the eigenvalues of such matrix are obtained. Namely, the result which can be obtained from Theorem 2 of [Bueno, A.C.F.: On r-circulant matrices with Fibonacci and Lucas numbers having arithmetic indices, AIP Conf. Proc. 1905 (2017), 030010] is improved because this result can not be applied in some cases. Since Theorem 4 in the same work relies on Theorem 2, the obtained formulae for the eigenvalues of a k-circulant matrix involving the Lucas numbers of even index show that there are cases when the result of Theorem 4 can also not be applied. Additionally, we present a more precise formula for the Euclidean norm of such matrix compared to the formula presented in Theorem 5 in the aforementioned reference. The upper and lower bounds for the spectral norm of a k-circulant matrix whose first row is
(Communicated by István Gaál)
Acknowledgement
We would like to thank the anonymous reviewer for his useful comments and suggestions that improved the quality of the manuscript.
References
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Articles in the same Issue
- Generalized Sasaki mappings in d0-Algebras
- On a theorem of Nathanson on Diophantine approximation
- Constructing infinite families of number fields with given indices from quintinomials
- Partitions into two Lehmer numbers in ℤq
- Fundamental systems of solutions of some linear differential equations of higher order
- On k-Circulant matrices involving the Lucas numbers of even index
- Explicit formulae for the Drazin inverse of the sum of two matrices
- On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
- Novel generalized tempered fractional integral inequalities for convexity property and applications
- Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
- The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
- Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
- Improvements on the Leighton oscillation theorem for second-order dynamic equations
- Topogenous orders on forms
- Comparison of topologies on fundamental groups with subgroup topology viewpoint
- An elementary proof of the generalized Itô formula
- Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
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