An observation on the determinant of a Sylvester-Kac type matrix

[1] R. Askey, Evaluation of Sylvester type determinants using orthogonal polynomials, In: H.G.W. Begehr et al. (eds.): Advances in analysis. Hack-ensack, NJ, World Scientific 2005, pp. 1-16.10.1142/9789812701732_0001Search in Google Scholar

[2] T. Boros, P. Rózsa, An explicit formula for singular values of the Sylvester-Kac matrix, Linear Algebra Appl. 421 (2007), 407-416.10.1016/j.laa.2006.10.008Search in Google Scholar

[3] W. Chu, Fibonacci polynomials and Sylvester determinant of tridiagonal matrix, Appl. Math. Comput. 216 (2010), 1018-1023.10.1016/j.amc.2010.01.089Search in Google Scholar

[4] W. Chu, X. Wang, Eigenvectors of tridiagonal matrices of Sylvester type, Calcolo 45 (2008), 217-233.10.1007/s10092-008-0153-4Search in Google Scholar

[5] P.A. Clement, A class of triple-diagonal matrices for test purposes, SIAM Rev. 1 (1959), 50-52.10.1137/1001006Search in Google Scholar

[6] A. Edelman, E. Kostlan, The road from Kac’s matrix to Kac’s random polynomials, in: J. Lewis (Ed.), Proc. of the Fifth SIAM Conf. on Applied Linear Algebra, SIAM, Philadelpia, 1994, pp. 503-507.Search in Google Scholar

[7] D.K. Faddeev, I.S. Sominskii, in: J.L. Brenner (Translator), Problems in Higher Algebra, Freeman, San Francisco, 1965.Search in Google Scholar

[8] C.M. da Fonseca, E. Kılıç, A new type of SylvesterKac matrix and its spectrum, Linear and Multilinear Algebra doi.org/10.1080/03081087.2019.1620673Search in Google Scholar

[9] C.M. da Fonseca, D.A. Mazilu, I. Mazilu, H.T. Williams, The eigenpairs of a Sylvester-Kac type matrix associated with a simple model for one-dimensional deposition and evaporation, Appl. Math. Lett. 26 (2013), 1206-1211.10.1016/j.aml.2013.06.006Search in Google Scholar

[10] O. Holtz, Evaluation of Sylvester type determinants using block-triangularization, In: H.G.W. Begehr et al. (eds.): Advances in analysis. Hackensack, NJ, World Scientific 2005, pp. 395-405.10.1142/9789812701732_0036Search in Google Scholar

[11] Z. Hu, P.B. Zhang, Determinants and characteristic polynomials of Lie algebras, Linear Algebra Appl. 563 (2019), 426-439.10.1016/j.laa.2018.11.015Search in Google Scholar

[12] Kh.D. Ikramov, On a remarkable property of a matrix of Mark Kac, Math. Notes 72 (2002), 325-330.10.1023/A:1020543219652Search in Google Scholar

[13] M. Kac, Random walk and the theory of Brownian motion, Amer. Math. Monthly 54 (1947), 369-391.10.1080/00029890.1947.11990189Search in Google Scholar

[14] E. Kılıç, Sylvester-tridiagonal matrix with alternating main diagonal entries and its spectra, Inter. J. Nonlinear Sci. Num. Simulation 14 (2013), 261-266.10.1515/ijnsns-2011-0068Search in Google Scholar

[15] E. Kılıç, T. Arıkan, Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix, Turk. J. Math. 40 (2016), 80-89.10.3906/mat-1503-46Search in Google Scholar

[16] T. Muir, The Theory of Determinants in the Historical Order of Development, vol. II, Dover Publications Inc., New York, 1960 (reprinted)Search in Google Scholar

[17] R. Oste, J. Van den Jeugt, Tridiagonal test matrices for eigenvalue computations: Two-parameter extensions of the Clement matrix, J. Comput. Appl. Math. 314 (2017), 30-39.10.1016/j.cam.2016.10.019Search in Google Scholar

[18] P. Rózsa, Remarks on the spectral decomposition of a stochastic matrix, Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 7 (1957), 199-206.Search in Google Scholar

[19] E. Schrödinger, Quantisierung als Eigenwertproblem III, Ann. Phys. 80 (1926), 437-490.10.1002/andp.19263851302Search in Google Scholar

[20] J.J. Sylvester, Théorème sur les déterminants de M. Sylvester, Nouvelles Ann. Math. 13 (1854), 305.Search in Google Scholar

[21] O. Taussky, J. Todd, Another look at a matrix of Mark Kac, Linear Algebra Appl. 150 (1991), 341-360.10.1016/0024-3795(91)90179-ZSearch in Google Scholar

[22] I. Vincze,Über das Ehrenfestsche Modell der Wärmeübertragung, Archi. Math XV (1964), 394-400.10.1007/BF01589220Search in Google Scholar