Leonard, I. E. The matrix exponential. (English) Zbl 0858.34009 SIAM Rev. 38, No. 3, 507-512 (1996). Summary: 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. Cited in 2 ReviewsCited in 20 Documents MSC: 34A30 Linear ordinary differential equations and systems Keywords:matrix exponential; linear differential equations PDFBibTeX XMLCite \textit{I. E. Leonard}, SIAM Rev. 38, No. 3, 507--512 (1996; Zbl 0858.34009) Full Text: DOI