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.
Highlights
Special matrices is a widely studied subject in matrix analysis
Special matrices whose entries are well known number sequences have become a very interesting research subject in recent years and many authors have obtained some good results in this area
The Pell and Pell-Lucas sequences Pn and Qn are defined by the recurrence relations
Summary
Special matrices is a widely studied subject in matrix analysis. Special matrices whose entries are well known number sequences have become a very interesting research subject in recent years and many authors have obtained some good results in this area. The norms of Toeplitz, Hankel and Circulant matrices involving Fibonacci, Lucas, Pell and Pell-Lucas numbers were investigated in [1, 2, 5, 6, 7]. We derive some sum formulas for the squares of Pell and Pell-Lucas numbers.
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