Let us define ？to be a ？r-Toeplitz matrix. The
entries in the first row of ？are ？or ;where Fn and Ln denote the usual Fibonacci
and Lucas numbers, respectively. We obtained some bounds for the spectral norm
of these matrices.
References
[1]
Dubbs, A. and Edelman, A. (2014) Infinite Random Matrix Theory. Tridiagonal Bordered Toeplitz Matrices and the Moment Problem. arXiv:1502.04931v1.
[2]
Erbas, C. and Tanik, M.M. (1995) Generating Solutions to the N-Queens Problems Using 2-Circulants. Mathematics Magazine, 68, 343-356. http://dx.doi.org/10.2307/2690923
[3]
Ngondiep, E., Serra-Capizzano, S. and Sesana, D. (2010) Spectral Features and Asymptotic Proporties for g-Circulant and g-Toeplitz Sequence. SIAM Journal on Matrix Analysis and Applications, 31, 1663-1687. http://dx.doi.org/10.1137/090760209
[4]
Szegö, G. (1958) Toeplitz Forms and Their Applications. University of California Press.
[5]
Hudson, R.E., Reed, C.W., Chen, D. and Lorenzelli, F. (1998) Blind Beamforming on a Randomly Distributed sensor Array System. Journal on Selected Areas in Communications, 16, 1555-1567.
[6]
Gray, R.M. and Davisson, L.D. (2005) An Introduction to Statistical Signal Processing. Cambridge University Press, London.
[7]
Wei, Y., Cai, J. and Ng, M.K. (2004) Computing Moore-Penrose Inverses of Toeplitz Matrices by Newton’s Iteration. Mathematical and Computer Modelling, 40, 181-191. http://dx.doi.org/10.1016/j.mcm.2003.09.036
[8]
Chou, W.S., Du, B.S. and Shiue, P.J.-S. (2008) A Note on Circulant Transition Matrices in Markov Chains. Linear Algebra and Its Applications, 429, 1699-1704. http://dx.doi.org/10.1016/j.laa.2008.05.004
[9]
Akbulak, M. and Bozkurt, D. (2008) On the Norms of Toeplitz Matrices Involving Fibonacci and Lucas Numbers. Hacettepe Journal of Mathematics and Statistics, 37, 89-95.
[10]
Shen, S. (2012) On the Norms of Toeplitz Matrices Involving k-Fibonacci and k-Lucas Numbers. International Journal of Contemporary Mathematical Sciences, 7, 363-368.
[11]
Vajda, S. (1989) Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications. Ellis Horwood Ltd.
[12]
Koshy, T. (2001) Fibonacci and Lucas Numbers with Applications. A Wiley-Interscience Publication.
[13]
Horn, R.A. and Johnson, C.R. (1991) Topics in Matrix Analysis. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511840371
![\"\"](\"Edit_39f585ad-de14-40d0-8d39-d98c1ad0f7f3.bmp\")
？to be a ![\"\"](\"Edit_ec4c9d4c-1a55-4ccd-ae86-021e04f8d245.bmp\")
？r-Toeplitz matrix. The
entries in the first row of ![\"\"](\"Edit_bce100c8-cff4-4526-911f-d7e12402271b.bmp\")
？are ![\"\"](\"Edit_77c59349-89cc-45f6-a168-b173f07abe64.bmp\")
？or ![\"\"](\"Edit_5bb5ce1d-86d1-40f5-9e47-8ec6b4d9e63b.bmp\")
;where Fn and Ln denote the usual Fibonacci
and Lucas numbers, respectively. We obtained some bounds for the spectral norm
of these matrices.
