TY - JOUR

T1 - Closed-form expressions for the matrix exponential

AU - De Zela, F.

N1 - Publisher Copyright:
© 2014 by the authors.

PY - 2014

Y1 - 2014

N2 - We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley-Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to physicists. Here, we derive the results on which the method is based by using tools most commonly employed by physicists. We show the advantages of the method in comparison with standard approaches, especially when dealing with the exponential of low-dimensional matrices. In contrast to other approaches that require, e.g., solving differential equations, the present method only requires the construction of the inverse of the Vandermonde matrix. We show the advantages of the method by applying it to different cases, mostly restricting the calculational effort to the handling of two-by-two matrices.

AB - We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley-Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to physicists. Here, we derive the results on which the method is based by using tools most commonly employed by physicists. We show the advantages of the method in comparison with standard approaches, especially when dealing with the exponential of low-dimensional matrices. In contrast to other approaches that require, e.g., solving differential equations, the present method only requires the construction of the inverse of the Vandermonde matrix. We show the advantages of the method by applying it to different cases, mostly restricting the calculational effort to the handling of two-by-two matrices.

KW - Cayley-Hamilton theorem

KW - Matrix exponential

KW - Two-by-two representations

KW - Vandermonde matrices

UR - http://www.scopus.com/inward/record.url?scp=84988443396&partnerID=8YFLogxK

U2 - 10.3390/sym6020329

DO - 10.3390/sym6020329

M3 - Article

AN - SCOPUS:84988443396

SN - 2073-8994

VL - 6

SP - 329

EP - 344

JO - Symmetry

JF - Symmetry

IS - 2

ER -