Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 2, Issue 1, April 2018, pp 1-4

Trace of the Laplace transform of exp(t Anxn)

J. López-Bonilla, R. López-Vázquez and S. Vidal-Beltrán

ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, México


We study the trace of the Laplace transform of exp(t A_nxn) in terms of the Faddeev’s matrices and the characteristic polynomial of A. Our expressions are in harmony with the results of Shui-Hung Hou..


Matrix exponential function, Characteristic polynomial, Faddeev’s matrices, Laplace transform.



1. L. Debnath, D. Bhatta, Integral transforms and their applications, Chapman & Hall/CRC, London (2007).

2. C. Aguilar, B. Carvajal, J. López-Bonilla, A study of matrix exponential function, Siauliai Mathematical Seminar (Lithuania) 5, (13), (2010) 5-17.

3. B. Hanzon, R. Peeters, Computer algebra in systems theory, Dutch Institute of Systems and Control, Course Program 1999-2000.

4. Shui-Hung Hou, On the Leverrier-Faddeev algorithm, Electronic Proc. of Asia Tech. Conf. in Maths. (1998).

5. Shui-Hung Hou, A simple proof of the Leverrier-Faddeev characteristic polynomial algorithm, SIAM Rev. 40, No. 3 (1998) 706-709.

6. I. Guerrero, J. López-Bonilla, J. Rivera, Leverrier-Takeno coefficients for the characteristic polynomial of a matrix, J. Inst. Eng. (Nepal) 8, No. 1-2 (2011) 255-258.

7. D. K. Faddeev, I. S. Sominsky, Collection of problems on higher algebra, Moscow (1949).

8. V. N. Faddeeva, Computational methods of linear algebra, Dover, New York (1959) Chap. 3.

9. D. K. Faddeev, Methods in linear algebra, W. H. Freeman, San Francisco, USA (1963).

10. J. C. Gower, A modified Leverrier-Faddeev algorithm for matrices with multiple eigenvalues, Linear Algebra and its Applications 31, No. 1 (1980) 61-70

11. J. H. Caltenco, J. López-Bonilla, R. Peña-Rivero, Characteristic polynomial of A and Faddeev’s method for A-1, Educatia Matematica 3, No. 1-2 (2007) 107-112.

12. A. Domínguez-Pacheco, J. López-Bonilla, S. Vidal-Beltrán, Inverse matrix and eigenvalue problem via Leverrier-Faddeev’s method, Prespacetime Journal 9, No. 1 (2018) to appear.

13. A. K. Hazra, Matrix: Algebra, calculus and generalized inverse, Cambridge Int. Sci. Pub. (2006).

14. F. B. Hildebrand, Methods of applied mathematics, Prentice-Hall, New York (1965).

15. J. L. Synge, Regular null networks in flat space-time, Proc. Roy. Irish Acad. A66 (1968) 41-68.

16. U. J. J. Leverrier, Sur les variations séculaires des éléments elliptiques des sept planétes principles, J. de Math. Pures Appl. Série 1, 5 (1840) 220-254

17. A. N. Krylov, On the numerical solution of the equation, that in technical problems, determines the small oscillation frequencies of material systems, Bull. de l’Acad. Sci. URSS 7, No. 4 (1931) 491-539.

18. H. Takeno, A theorem concerning the characteristic equation of the matrix of a tensor of the second order, Tensor NS 3 (1954) 119-122.

19. E. B. Wilson, J. C. Decius, P. C. Cross, Molecular vibrations, Dover, New York (1980) 216-217.

Visitors count

Join us