Some norm inequalities for special Gram matrices

Ramazan Türkmen 1 , Osman Kan 2 ,  and Hasan Gökbas 3
  • 1 Science Faculty, Selcuk University, 42031 Konya, Turkey
  • 2 Mustafa Bagriacik of Secondary School, Konya, Konya, Turkey
  • 3 Semsi Tebrizi Anatolian Religious Vocational High School, Konya, Turkey

Abstract

In this paper we firstly give majorization relations between the vectors Fn = {f0, f1, . . . , fn−1},Ln = {l0, l1, . . . , ln−1} and Pn = {p0, p1, . . . , pn−1} which constructed with fibonacci, lucas and pell numbers. Then we give upper and lower bounds for determinants, Euclidean norms and Spectral norms of Gram matrices GF=〈Fn,Fni〉, GL=〈Ln,Lni〉, GP=〈Pn,Pni〉, GFL=〈Fn,Lni〉, GFP=〈Fn,Pni〉.

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