Matrix Functions of Exponential Order

Author(s)
Mithat Idemen

ABSTRACT

Both the theoretical and practical investigations of various dynamical systems need to extend the definitions of various functions defined on the real axis to the set of matrices. To this end one uses mainly three methods which are based on 1) the Jordan canonical forms, 2) the polynomial interpolation, and 3) the Cauchy integral formula. All these methods give the same result, say *g( A)*, when they are applicable to given function

Cite this paper

M. Idemen, "Matrix Functions of Exponential Order,"*Applied Mathematics*, Vol. 4 No. 9, 2013, pp. 1260-1268. doi: 10.4236/am.2013.49170.

M. Idemen, "Matrix Functions of Exponential Order,"

References

[1] A. Cayley, “A Memoir on the Theory of Matrices,” Philosophical Transactions of the Royal Society of London, Vol. 148, 1858, pp. 17-37. doi:10.1098/rstl.1858.0002

[2] N. J. Higham, “Functions of Matrices: Theory and Com putation,” Society for Industrial and Applied Mathe matica (SIAM), Philadelphia, 2008.

[3] N. I. Mushkhelishvili, “Singular Integral Equations,” P. Noordhoff Ltd., Holland, 1958.

[4] E. C. Titchmarsh, “Introduction to the Theory of Fourier Integrals,” Chelsea Publishing Company, 1986, Chapter 1.3.

[1] A. Cayley, “A Memoir on the Theory of Matrices,” Philosophical Transactions of the Royal Society of London, Vol. 148, 1858, pp. 17-37. doi:10.1098/rstl.1858.0002

[2] N. J. Higham, “Functions of Matrices: Theory and Com putation,” Society for Industrial and Applied Mathe matica (SIAM), Philadelphia, 2008.

[3] N. I. Mushkhelishvili, “Singular Integral Equations,” P. Noordhoff Ltd., Holland, 1958.

[4] E. C. Titchmarsh, “Introduction to the Theory of Fourier Integrals,” Chelsea Publishing Company, 1986, Chapter 1.3.