CIRCULANT, NEGACYCLIC AND SEMICIRCULANT MATRICES WITH THE MODIFIED PELL, JACOBSTHAL AND JACOBSTHAL-LUCAS NUMBERS

Abstract

CIRCULANT, NEGACYCLIC AND SEMICIRCULANT MATRICES WITH THE MODIFIED PELL, JACOBSTHAL AND JACOBSTHAL-LUCAS NUMBERS

Abstract

In this paper, we give some properties of the modified Pell, Jacobsthal and Jacobsthal-Lucas numbers. We then define the circulant, negacyclic and semicirculant matrices with these numbers and investigate the norms, eigenvalues and determinants of these matrices.

Keywords

• Modified Pell numbers
• Jacobsthal numbers
• Jacobsthal -Lucas numbers
• Circulant Matrix
• 2000 AMS Classification: Primary: 15 A 60

References

1. Davis, P. J. Circulant Matrices (John Wiley&Sons, New York, 1979).
2. Frey, D. D. and Sellers, J. A. Jacobsthal numbers and alternating sign matrices, Journal of Integer Sequences 3 (2),1–16, 2001.
3. Horadam, A. F. Jacobsthal and Pell curves, The Fibonacci Quarterly 26,77–83, 1988.
4. Horadam, A. F. Applications of modified Pell numbers to representations, Ulam Quarterly 3(1), 34–53, 1994.
5. Horadam, A. F. Jacobsthal represantation numbers, The Fibonacci Quarterly 34 (1), 40–53, 1996.
6. Horn, R. A. Johnson, C. R. Matrix Analysis (Cambridge University Press, 1985).
7. Karner, H., Schneid, J. C. and Ueberhuber, W. Spectral decomposition of real circulant ma- trices, Lin. Alg. Appl. 367, 301–311, 2003.