Integers Powers of Certain Asymmetric Matrices
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
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Physical Communication
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There are many different methods to calculate the exponential of a matrix: series methods, differential equations methods, polynomial methods, matrix decomposition methods, and splitting methods, none of which is entirely satisfactory from either a theoretical or a computational point of view. How then should the matrix exponential be introduced in an elementary differential equations course, for engineering students for example, with a minimum of mathematical prerequisites? In this note, a method is given that uses the students' knowledge of homogeneous linear differential equations with constant coefficients and the Cayley--Hamilton theorem. The method is not new; what is new is the approach.