Norms Of Hankel-Hessenberg and Toeplitz-Hessenberg Matrices Involving Pell and Pell-Lucas Numbers
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2016, Vol 12, Issue 11
Abstract
We derive some sum formulas for the squares of Pell and Pell-Lucas numbers. We construct Hankel-Hessenberg andToeplitz-Hessenberg matrices whose entries in the first column are HHP = aij , ij i j a Pï€ = ; Q HH =   ij a , ij i j a Qï€ =and P TH =   ij a , 1 = ij iï€ j a P ; Q TH =   ij a , 1 = ij iï€ j a Q , respectively where n P and n Q denote the usual Pell and Pell-Lucas numbers. Then, we found upper and lower bounds for spectral norm of these matrices.
Authors and Affiliations
Hasan GÖKBAS
Keywords
Related Articles
- EP ID EP651713
- DOI 10.24297/jam.v12i11.22
- Views 183
- Downloads 0
Karp's Theorem in Inverse Obstacle Scattering Problems
In this work, we provide a proof of the so-called Karp's theorem in a different approach. We use the unique continuation principle together with the monotonicity of eigenvalues for the negative Laplace operator...
An analytic approximate solution of the matrix Riccati differential equation arising from the LQ optimal control problems
Approximate analytical solution of the matrix Riccati differential equation related to the linear quadratic optimal control problems, is the main goal of this paper which has a specific importance in the optimal control...
Model Higgs Bundles in Exceptional Components of the Sp(4,R)-Character Variety
We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the Sp(4,R)-Hitchin equations using the linearization of a relevant elliptic operato...
Oscillation and Nonoscillation of Fourth-order Nonlinear Neutral Differential Equations with "Maxima".
In this paper, we study the oscillation and asymptotic properties of fourth-order nonlinear neutral dierential equations with \maxima" (r(t)(y(t) + p(t)y(h(t)))00)00 + q(t) max [(t);t] f(y(s)) = 0; t t0 0 (0.1)...
The Natural Lift Curve and Geodesic Sprays in Euclidean 4-Space
In this work, we presented the natural lift curves of the spherical indicatrices of a curve in E4. Also, some interesting results about the original curve were obtained depending on the assumption that the natural lift c...