442
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

A new type of Sylvester–Kac matrix and its spectrum

ORCID Icon &
Pages 1072-1082 | Received 29 Jan 2019, Accepted 15 May 2019, Published online: 27 May 2019

References

  • Sylvester JJ. Théorème sur les déterminants de M. Sylvester. Nouvelles Ann Math. 1854;13:305.
  • Muir T. The theory of determinants in the historical order of development. vol. II. New York: Dover Publications; 1960. (reprinted).
  • da Fonseca CM, Mazilu DA, Mazilu I, et al. The eigenpairs of a Sylvester-Kac type matrix associated with a simple model for one-dimensional deposition and evaporation. Appl Math Lett. 2013;26:1206–1211. doi: 10.1016/j.aml.2013.06.006
  • Kac M. Random walk and the theory of Brownian motion. Amer Math Monthly. 1947;54:369–391. doi: 10.1080/00029890.1947.11990189
  • Taussky O, Todd J. Another look at a matrix of Mark Kac. Linear Algebra Appl. 1991;150:341–360. doi: 10.1016/0024-3795(91)90179-Z
  • da Fonseca CM, Kılıç E. An observation on the determinant of a Sylvester-Kac type matrix, An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat., accepted for publication.
  • Holtz O. Evaluation of Sylvester type determinants using block-triangularization. In: Begehr HGW, et al. editor. Advances in analysis. Hackensack, NJ: World Scientific; 2005. p. 395–405.
  • Askey R. Evaluation of Sylvester type determinants using orthogonal polynomials. In: Begehr HGW, et al. editor. Advances in analysis. Hackensack, NJ: World Scientific; 2005, p. 1–16.
  • Boros T, Rózsa P. An explicit formula for singular values of the Sylvester-Kac matrix. Linear Algebra Appl. 2007;421:407–416. doi: 10.1016/j.laa.2006.10.008
  • Clement PA. A class of triple-diagonal matrices for test purposes. SIAM Rev. 1959;1:50–52. doi: 10.1137/1001006
  • Chu W, Wang X. Eigenvectors of tridiagonal matrices of Sylvester type. Calcolo. 2008;45:217–233. doi: 10.1007/s10092-008-0153-4
  • Edelman A, Kostlan E. The road from Kac's matrix to Kac's random polynomials. In: Lewis J, editor. Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, Philadelphia: SIAM; 1994. p. 503–507.
  • Ikramov KhD. On a remarkable property of a matrix of Mark Kac. Math Notes. 2002;72:325–330. doi: 10.1023/A:1020543219652
  • Rózsa P. Remarks on the spectral decomposition of a stochastic matrix. Magyar Tud Akad Mat Fiz Oszt Közl. 1957;7:199–206.
  • Schrödinger E. Quantisierung als Eigenwertproblem III. Ann Phys. 1926;80:437–490. doi: 10.1002/andp.19263851302
  • Vincze I. Über das Ehrenfestsche Modell der Wärmeübertragung. Archi Math. 1964;XV:394–400. doi: 10.1007/BF01589220
  • Chu W. Fibonacci polynomials and Sylvester determinant of tridiagonal matrix. Appl Math Comput. 2010;216:1018–1023.
  • Kılıç E, Arıkan T. Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix. Turk J Math. 2016;40:80–89. doi: 10.3906/mat-1503-46
  • Oste R, Van den Jeugt J. Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix. J Comput Appl Math. 2017;314:30–39. doi: 10.1016/j.cam.2016.10.019
  • Kılıç E. Sylvester-tridiagonal matrix with alternating main diagonal entries and its spectra. Inter J Nonlinear Sci Num Simulation. 2013;14:261–266.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.