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2016 | 4 | 1 | 262-269
Tytuł artykułu

Some norm inequalities for special Gram matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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〉.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
262-269
Opis fizyczny
Daty
otrzymano
2016-01-13
zaakceptowano
2016-06-08
online
2016-07-04
Twórcy
  • Science Faculty, Selcuk University, 42031 Konya, Turkey
autor
  • Mustafa Bagriacik of Secondary School, Konya, Konya, Turkey
  • Semsi Tebrizi Anatolian Religious Vocational High School, Konya, Turkey
Bibliografia
  • [1] R. Türkmen and H. Civciv, Notes on norms circulant matrices with Lucas numbers, Int. J. Inf. Sciences, Vol. 4 No. 1, 142-147, 2008.
  • [2] S. Solak, On the norms of circulantmatrices with the Fibonacci and Lucas numbers, Appl.Math. Comput. 160,125-132, 2005. [WoS]
  • [3] D. Bozkurt and Tin Y. Tam, Determinants and inverses of r-circulant matrices associated with a number sequence Linear Multilinear Algebra, 2014. [WoS]
  • [4] S. Shen and J. Cen, On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers, Int. J. Contemp. Math. Sciences Vol. 5 No 12, 569-578, 2010.
  • [5] F. Zhang, Matrix Theory: Basic and Techniques,Springer-Verlag, New York, 1999.
  • [6] V. Sreeram, P. Agathoklis, On the Properties of Gram Matrix, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, Vol. 41, No. 3, 1994.
  • [7] V.K. Jain and R.D Gupta, Identification of linear systems through a Gramian technique, Int. J. Cont., Vol. 12, pp.421-431, 1970.
  • [8] V.K. Jain, Filter Analysis by use of pencil of functions: Part I, IEEE Trans. Circuits and Systems, Vol. CAS-21, pp. 574-579, 1974.
  • [9] V.K. Jain, Filter Analysis by use of pencil of functions: Part II, IEEE Trans. Circuits and Systems, Vol. CAS-21, pp. 580-583, 1974.
  • [10] T.N. Lucas, Evaluation of scalar products of repeated integrals by routh algorithm, Electron. Lett., Vol.24. pp.1290-1291, 1988.
  • [11] T. Koshy, Fibonacci and Lucas Numbers with applications, John Wiley & Sons, Inc., 2001.
  • [12] T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer, 2014.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0026
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