Norms Of Hankel-Hessenberg and Toeplitz-Hessenberg Matrices Involving Pell and Pell-Lucas Numbers
DOI:
https://doi.org/10.24297/jam.v12i11.22Keywords:
Euclidean norm, Spectral norm, Toeplitz matrix, Hankel matrix, Hessenberg matrix, Pell numbers, Pell- Lucas numbers.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.
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References
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Journal of Mathematics and Statistics, 37(2), 89-95, (2008).
[2] M. Bah s i, S. Solak, On the norms of r-circulant matrices with the hyper-Fibonacci and Lucas numbers, Journal of
Mathematical Inequalities, 8(4), 693-705, (2014).
[3] M. Merca, A Note On The Determinant Of a Toeplitz-Hessenberg Matrix, Special Matrices, DOI: 10.2478/spma-2013-
0003, (2013).
[4] R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, New York, (1991).
[5] H. Civciv, R. Türkmen, Notes on norms of circulant matrices with lucas numbers, Int. Jour. of Inf. and Systems
Sciences, 4(1), 142-147, (2008).
[6] R. Türkmen, H. Gökba s , On the Spectral Norm of r -Circulant Matrices with Pell and Pell-Lucas numbers, Journal of
Inequalities and Applications, 2016:65, DOI: 10.1186/s13660-016-0997-0, (2016).
[7] S. Shen, J. Cen, On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers, Int. J.
Contemp. Math. Sciences, 5(12), 569-578, (2010).
[8] T. Koshy, Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, (2001).
[9] T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer, New York, (2014).
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Published
2016-12-30
How to Cite
GÖKBAS, H. (2016). Norms Of Hankel-Hessenberg and Toeplitz-Hessenberg Matrices Involving Pell and Pell-Lucas Numbers. JOURNAL OF ADVANCES IN MATHEMATICS, 12(11), 6799–6806. https://doi.org/10.24297/jam.v12i11.22
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