Transformations computations‎: ‎Power‎, ‎Roots and Inverse

Subject Areas : Complex Analysis

M. Ghorbanzadeh ¹ , H. Kamali ² , A. Mansoori ³

1 - Department of Basic Science, Imam Reza International University, Mashhad, Iran
2 - Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
3 - Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Received: 2017-02-23 Accepted : 2018-02-10 Published : 2018-03-01

Keywords: &lrm, &lrm, Annihilated elements&lrm, , &lrm, matrix power&lrm, , &lrm, inverse matrix&lrm, , &lrm, matrix roots&lrm, &rlm, ,

Abstract :

‎This paper presents some results of an annihilated element in Banach algebra‎, ‎and in specific case‎, ‎for any square matrix‎. The developed method significantly improves the computational aspects of transformations calculus and especially for finding powers and roots of any annihilated element‎. ‎An example is given to compare the proposed method with some other methods to show the efficiency and performance‎.

References:

[1] G. H. Golub, C. F. Van Loan, Matrix computations, JHU Press, 1983.

[2] N. J. Higham, Functions of matrices: theory and computation, SIAM, 2008.

[3] T. Li, Z. Zhang, T. Wang, Determining the structure of the Jordan normal form of a matrix by symbolic computation, Linear Algebra and its Applications. 252 (1-3) (1997), 221-259.

[4] J. M. Ortega, Matrix theory: A second course, Springer Science & Business Media, 2013.

[5] J. J. Palis, W. De Melo, Geometric theory of dynamical systems: an introduction, Springer Science & Business Media, 2012.

[6] R. Penrose, A generalized inverse for matrices, Math. Proc. Camb. Philos. Soc. 51 (3) (1955), 406-413.

[7] W. Rudin, Functional Analysis, Internat. Ser. Pure. Appl. Math., 1991.

[8] E. Suli, D. F. Mayers, An introduction to numerical analysis, Cambridge University Press, 2003.

[9] M. Tomas-Rodriguez, S. P. Banks, Linear time-varying approximations to nonlinear dynamical systems: with applications in control and optimization, Springer Science & Business Media, 2010.

[10] J. H. Van Lint, R. M. Wilson, A course in combinatorics, Cambridge University Press, 2001.