Some norm inequalities for special Gram matrices

Ramazan Türkmen; Osman Kan; Hasan Gökbas

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 262-269
  • ISSN: 2300-7451

Abstract

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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〉.

How to cite

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Ramazan Türkmen, Osman Kan, and Hasan Gökbas. "Some norm inequalities for special Gram matrices." Special Matrices 4.1 (2016): 262-269. <http://eudml.org/doc/285565>.

@article{RamazanTürkmen2016,
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〉.},
author = {Ramazan Türkmen, Osman Kan, Hasan Gökbas},
journal = {Special Matrices},
keywords = {Gram matrix; Matrix norms; Fibonacci; Lucas and Pell Numbers; matrix norms; Lucas and Pell numbers},
language = {eng},
number = {1},
pages = {262-269},
title = {Some norm inequalities for special Gram matrices},
url = {http://eudml.org/doc/285565},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Ramazan Türkmen
AU - Osman Kan
AU - Hasan Gökbas
TI - Some norm inequalities for special Gram matrices
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 262
EP - 269
AB - 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〉.
LA - eng
KW - Gram matrix; Matrix norms; Fibonacci; Lucas and Pell Numbers; matrix norms; Lucas and Pell numbers
UR - http://eudml.org/doc/285565
ER -

References

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  4. [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.  Zbl1198.15016
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  7. [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.  Zbl0204.46203
  8. [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. [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.  
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  11. [11] T. Koshy, Fibonacci and Lucas Numbers with applications, John Wiley & Sons, Inc., 2001.  Zbl0984.11010
  12. [12] T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer, 2014.  Zbl1330.11002

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