Some norm inequalities for special Gram matrices

• Autorzy: Ramazan Türkmen , Osman Kan , Hasan Gökbas
• 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

EN

Gram matrix; Matrix norms; Fibonacci; Lucas and Pell Numbers

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 262-269

Daty

otrzymano

2016-01-13

zaakceptowano

2016-06-08

online

2016-07-04

Twórcy

autor

Ramazan Türkmen

• Science Faculty, Selcuk University, 42031 Konya, Turkey

autor

Osman Kan

• Mustafa Bagriacik of Secondary School, Konya, Konya, Turkey

autor

Hasan Gökbas

• Semsi Tebrizi Anatolian Religious Vocational High School, Konya, Turkey

Bibliografia

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• [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.
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• [12] T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer, 2014.

Identyfikatory

DOI

10.1515/spma-2016-0026