2021 The exponential matrix: an explicit formula by an elementary method
Oswaldo Rio Branco de Oliveira
Author Affiliations +
Real Anal. Exchange 46(1): 99-106 (2021). DOI: 10.14321/realanalexch.46.1.0099

Abstract

We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of a real and finite square matrix $A$ (and for complex ones also). The elementary method developed avoids Jordan canonical form, eigenvectors, resolution of any linear system, matrix inversion, polynomial interpolation, complex integration, functional analysis, and generalized Fibonacci sequences. The basic tools are the Cayley-Hamilton theorem and the method of partial fraction decomposition. Two examples are given. We also show that such method applies to algebraic operators on infinite dimensional real Banach spaces.

Citation

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Oswaldo Rio Branco de Oliveira. "The exponential matrix: an explicit formula by an elementary method." Real Anal. Exchange 46 (1) 99 - 106, 2021. https://doi.org/10.14321/realanalexch.46.1.0099

Information

Published: 2021
First available in Project Euclid: 14 October 2021

Digital Object Identifier: 10.14321/realanalexch.46.1.0099

Subjects:
Primary: 15-01 , 34-01
Secondary: 15A16 , 34A30 , 47A60 , 65F60

Keywords: exponential matrix , functional calculus , functions of matrices , linear equations and systems , ordinary differential equations

Rights: Copyright © 2021 Michigan State University Press

Vol.46 • No. 1 • 2021
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