Details

SOME CONDITION REGARDING TO COMMUTING AND NON COMMUTING EXPONENTIAL MATRIX

Mohammed Abdullah Salman

Department of Mathematics & Statistics, Yeshwant Mahavidyalaya, Swami Ramamnand Teerth Marthwada University, Nanded, India.

V C Borkar

Department of Mathematics & Statistics, Yeshwant Mahavidyalaya, Swami Ramamnand Teerth Marthwada University, Nanded, India.

107-118

Vol: 6, Issue: 2, 2016

Receiving Date: 2016-03-07 Acceptance Date:

2016-04-05

Publication Date:

2016-05-08

Download PDF

Abstract

Accordingly to the previous paper for authors [1]. The exponential function defined on noncommutative algebra but does not occur in the general form of equation x y x y e  e e  . In this paper we define the conditions for which this equation is valid in M(2,R) , it will show it more easily and it shows some science achievements over 50’s.

Keywords: Matrix Exponential, Commuting Matrix, Non-commuting Matrix

References

  1. Mohammed Abdullah Salman and Borkar, V. C. New Method to Compute Commuting and Noncommuting Exponential Matrix, International Journal of Current Research Vol. 8, Issue, 01, pp. xxx-xxxx, January, 2016
  2. Morinaga K - Nono T.(1954) On the non-commutative solutions of the exponential equation x y x y e  e e  . J. Sci. Hiroshima Univ. (A) 17 345-358.
  3. Bourgeois G. (2007) On commuting exponentials in low dimensions. Linear Algebra Appl. 423 277-286.
  4. Clement de Seguins Pazzis (2011) A condition on the powers of exp(A) and exp (B) that implies AB = BA. arXIV: 1012.4420v3.
  5. Nathelie Smalls, The exponential of matrices, 2007, Master Thesis, University of Georgia, Georgia, 49 pp.
  6. Cleve Moler, Charles Van Loan (2003) Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later SIAM Review, Volume 20, Number 4, 1978, pages 801–836.
  7. N. J. Higham, Functions of Matrices Theory and Computation, SIAM, Society for Industrial and Applied Mathematics, Philadelphia, A. USA, 2008. ISBN 978-0-89871- 646-7. xx+425 pp.
  8. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991,ISBN 978-0-521- 46713-1 , viii+607 pp.
  9. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press,1985, ISBN 0-521-30586-2, xiii+561 pp.
  10. Syed Muhammad Ghufran,The Computation of Matrix Functions in Particular The Matrix Exponential, Master Thesis, University of Birmingham,England,2009,169 pp.
  11. R. Bellman, Introduction to Matrix Analysis, 2nd ed. New York: McGraw- Hill,1960, reprinted by SIAM, Philadelphia,1995.
  12. Nicholas J.Higham and AwadH. Al-Mohy, Computing Matrix Functions, Manchester Institute for Mathematical Sciences 2010,The University of Manchester, ISSN 1749-9097.pp1-47
  13. Denssis S. Bernstein and Wasin So, Some explicit formulas for the matrix exponential, IEEE transaction on Automatic control,vol38.No 8,August 1993.
Back

Disclaimer: All papers published in IJRST will be indexed on Google Search Engine as per their policy.

We are one of the best in the field of watches and we take care of the needs of our customers and produce replica watches of very good quality as per their demands.