Next Article in Journal
Dynamic Processes in Prochiral Solvating Agents (pro-CSAs) Studied by NMR Spectroscopy
Next Article in Special Issue
Invisibility and PT Symmetry: A Simple Geometrical Viewpoint
Previous Article in Journal
The Almost Periodic Rigidity of Crystallographic Bar-Joint Frameworks
Previous Article in Special Issue
Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
Open AccessArticle

Closed-Form Expressions for the Matrix Exponential

Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Ap. 1761,Lima L32, Peru
Symmetry 2014, 6(2), 329-344; https://doi.org/10.3390/sym6020329
Received: 28 February 2014 / Revised: 16 April 2014 / Accepted: 17 April 2014 / Published: 29 April 2014
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
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. View Full-Text
Keywords: matrix exponential; Cayley–Hamilton theorem; two-by-two representations; Vandermonde matrices matrix exponential; Cayley–Hamilton theorem; two-by-two representations; Vandermonde matrices
MDPI and ACS Style

De Zela, F. Closed-Form Expressions for the Matrix Exponential. Symmetry 2014, 6, 329-344.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Only visits after 24 November 2015 are recorded.
Back to TopTop