Preferences help
enabled [disable] Abstract
Number of results
2018 | 102 | 166-172
Article title

An alternative to Gower’s inverse matrix

Title variants
Languages of publication
We show that the Faddeev-Sominsky’s process allows construct a natural inverse for any square matrix, which is an alternative to the inverse obtained by Gower.
Physical description
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, México
  • ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, México
  • [1] C. Lanczos, Applied analysis, Dover, New York (1988).
  • [2] L. Hogben, Handbook of linear algebra, Chapman & Hall / CRC Press, London (2006).
  • [3] A. K. Hazra, Matrix: Algebra, calculus and generalized inverse, Cambridge Int. Sci. Pub. (2006).
  • [4] H. Wayland, Expansion of determinantal equations into polynomial form. Quart. Appl. Math. 2 (1945) 277-306.
  • [5] A. S. Householder, F. L. Bauer, On certain methods for expanding the characteristic polynomial. Numerische Math. 1 (1959) 29-37.
  • [6] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford (1965).
  • [7] D. Lovelock, H. Rund, Tensors, differential forms, and variational principles, John Wiley and Sons, New York (1975).
  • [8] U. J. J. Leverrier, Sur les variations séculaires des éléments elliptiques des sept planétes principales. J. de Math. Pures Appl. Série 1, 5 (1840) 220-254.
  • [9] 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.
  • [10] H. Takeno, A theorem concerning the characteristic equation of the matrix of a tensor of the second order, Tensor NS 3 (1954) 119-122.
  • [11] E. B. Wilson, J. C. Decius, P. C. Cross, Molecular vibrations, Dover, New York (1980) 216-217.
  • [12] I. Guerrero-Moreno, J. López-Bonilla, J. Rivera-Rebolledo, Leverrier-Takeno coefficients for the characteristic polynomial of a matrix. J. Inst. Eng. 8, No. 1-2 (2011) 255-258.
  • [13] D. K. Faddeev, I. S. Sominsky, Collection of problems on higher algebra, Moscow (1949).
  • [14] V. N. Faddeeva, Computational methods of linear algebra, Dover, New York (1959) Chap. 3.
  • [15] D. K. Faddeev, Methods in linear algebra, W. H. Freeman, San Francisco, USA (1963).
  • [16] 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.
  • [17] M. Zuhair Nashed (Ed.), Generalized inverses and applications, Academic Press, New York (1976).
  • [18] A. Ben-Israel, T. N. E. Greville, Generalized inverses: Theory and applications, Springer-Verlag, New York (2003).
  • [19] J. C. Gower, A modified Leverrier-Faddeev algorithm for matrices with multiple eigenvalues. Linear Algebra and its Applications 31, No. 1 (1980) 61-70.
  • [20] L. S. Brown, Quantum field theory, Cambridge University Press (1994).
  • [21] T. L. Curtright, D. B. Fairlie, A Galileon primer, arXiv: 1212.6972v1 [hep-th] 31 Dec. 2012.
  • [22] B. Hanzon, R. Peeters, Computer algebra in systems theory, Dutch Institute of Systems and Control, Course Program 1999-2000.
  • [23] R. Cruz-Santiago, J. López-Bonilla, S. Vidal-Beltrán, On eigenvectors associated to a multiple eigenvalue, World Scientific News 100 (2018) 248-253.
  • [24] G. Helmberg, P. Wagner, G. Veltkamp, On Faddeev-Leverrier’s method for the computation of the characteristic polynomial of a matrix and of eigenvectors. Linear Algebra and its Applications 185 (1993) 219-233.
  • [25] A. S. Householder, The theory of matrices in numerical analysis, Blaisdell, New York (1964).
  • [26] J. M. Souriau, Une method pour la decomposition spectral et l’inversion des matrices. C. R. Acad. Sci. Paris 227 (1948) 1010-1011.
  • [27] J. S. Frame, A simple recursion formula for inverting a matrix. Bull. Amer. Math. Soc. 55 (1949) 1045.
  • [28] J. López-Bonilla, H. Núñez-Yépez, An identity for spacetimes embedded into E5. Pramana J. Phys. 46, No. 3 (1996) 219-221.
  • [29] J. López-Bonilla, J. Morales, G. Ovando, An identity for R4 embedded into E5. Indian J. Math. 42, No. 3 (2000) 309-312.
  • [30] J. López-Bonilla, J. Morales, G. Ovando, E. Ramírez, Leverrier-Faddeev’s algorithm applied to spacetimes of class one. Proc. Pakistan Acad. Sci. 43, No. 1 (2006) 47-50.
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.