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Linear algebra of the Lucas matrix

Yıl 2021, Cilt: 50 Sayı: 2, 549 - 558, 11.04.2021
https://doi.org/10.15672/hujms.746184

Öz

In this paper, we give the factorizations of the Lucas and inverse Lucas matrices. We also investigate the Cholesky factorization of the symmetric Lucas matrix. Moreover, we obtain the upper and lower bounds for the eigenvalues of the symmetric Lucas matrix by using some majorization techniques.

Kaynakça

  • [1] C.M. Fonseca and E. Kılıç, An observation on the determinant of a Sylvester-Kac type matrix, An. Univ. "Ovidius" Constanta Ser. Mat. 28 (1), 111–115, 2020.
  • [2] C.M. Fonseca and Kılıç, A new type of Sylvester–Kac matrix and its spectrum, https://doi.org/10.1080/03081087.2019.1620673.
  • [3] G.H. Hardy, J.E. Littlewood and G. Pólya, Some simple inequalities satisfied by con- vex functions, Messenger Math. 58, 145–152, 1929.
  • [4] C.R. Johnson and R.A. Horn, Matrix analysis, Cambridge University Press Cam- bridge, 1985.
  • [5] E. Kilic and D. Tasci, The linear algebra of the Pell matrix, Bol. Soc. Mat. Mex. 11 (3), 163–174, 2005.
  • [6] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2001.
  • [7] G.-Y. Lee, J.-S. Kim and S.-G. Lee, Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 40 (3), 203–211, 2002.
  • [8] G.-Y. Lee and J.-S. Kim, The linear algebra of the k−Fibonacci matrix, Linear Algebra Appl. 373, 75–87, 2003.
  • [9] A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: theory of majorization and its applications 143, Springer, 1979.
  • [10] P. Stanica, Cholesky factorizations of matrices associated with r−order recurrent se- quences, Integers, 5 (2), A16, 2005.
  • [11] Z. Zhang and Y. Zhang, The Lucas matrix and some combinatorial identities, Indian J. Pure Appl. Math. 38 (5), 457–465, 2007.
Yıl 2021, Cilt: 50 Sayı: 2, 549 - 558, 11.04.2021
https://doi.org/10.15672/hujms.746184

Öz

Kaynakça

  • [1] C.M. Fonseca and E. Kılıç, An observation on the determinant of a Sylvester-Kac type matrix, An. Univ. "Ovidius" Constanta Ser. Mat. 28 (1), 111–115, 2020.
  • [2] C.M. Fonseca and Kılıç, A new type of Sylvester–Kac matrix and its spectrum, https://doi.org/10.1080/03081087.2019.1620673.
  • [3] G.H. Hardy, J.E. Littlewood and G. Pólya, Some simple inequalities satisfied by con- vex functions, Messenger Math. 58, 145–152, 1929.
  • [4] C.R. Johnson and R.A. Horn, Matrix analysis, Cambridge University Press Cam- bridge, 1985.
  • [5] E. Kilic and D. Tasci, The linear algebra of the Pell matrix, Bol. Soc. Mat. Mex. 11 (3), 163–174, 2005.
  • [6] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2001.
  • [7] G.-Y. Lee, J.-S. Kim and S.-G. Lee, Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 40 (3), 203–211, 2002.
  • [8] G.-Y. Lee and J.-S. Kim, The linear algebra of the k−Fibonacci matrix, Linear Algebra Appl. 373, 75–87, 2003.
  • [9] A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: theory of majorization and its applications 143, Springer, 1979.
  • [10] P. Stanica, Cholesky factorizations of matrices associated with r−order recurrent se- quences, Integers, 5 (2), A16, 2005.
  • [11] Z. Zhang and Y. Zhang, The Lucas matrix and some combinatorial identities, Indian J. Pure Appl. Math. 38 (5), 457–465, 2007.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Nurettin Irmak 0000-0003-0409-4342

Cahit Köme 0000-0002-6488-9035

Yayımlanma Tarihi 11 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 2

Kaynak Göster

APA Irmak, N., & Köme, C. (2021). Linear algebra of the Lucas matrix. Hacettepe Journal of Mathematics and Statistics, 50(2), 549-558. https://doi.org/10.15672/hujms.746184
AMA Irmak N, Köme C. Linear algebra of the Lucas matrix. Hacettepe Journal of Mathematics and Statistics. Nisan 2021;50(2):549-558. doi:10.15672/hujms.746184
Chicago Irmak, Nurettin, ve Cahit Köme. “Linear Algebra of the Lucas Matrix”. Hacettepe Journal of Mathematics and Statistics 50, sy. 2 (Nisan 2021): 549-58. https://doi.org/10.15672/hujms.746184.
EndNote Irmak N, Köme C (01 Nisan 2021) Linear algebra of the Lucas matrix. Hacettepe Journal of Mathematics and Statistics 50 2 549–558.
IEEE N. Irmak ve C. Köme, “Linear algebra of the Lucas matrix”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, ss. 549–558, 2021, doi: 10.15672/hujms.746184.
ISNAD Irmak, Nurettin - Köme, Cahit. “Linear Algebra of the Lucas Matrix”. Hacettepe Journal of Mathematics and Statistics 50/2 (Nisan 2021), 549-558. https://doi.org/10.15672/hujms.746184.
JAMA Irmak N, Köme C. Linear algebra of the Lucas matrix. Hacettepe Journal of Mathematics and Statistics. 2021;50:549–558.
MLA Irmak, Nurettin ve Cahit Köme. “Linear Algebra of the Lucas Matrix”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, 2021, ss. 549-58, doi:10.15672/hujms.746184.
Vancouver Irmak N, Köme C. Linear algebra of the Lucas matrix. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):549-58.