Abstract
The matrix versions of the familiar real and complex exponential and logarithm functions are fundamental for the study of many aspects of matrix group theory, particularly the one-parameter subgroups. Indeed, the matrix exponential function provides the link between the Lie algebra of a matrix group and the group itself. In the case of a compact connected matrix group, the exponential is even surjective, allowing a parametrisation of such a group by a region in ℝn for some n; see Chapter 10 for details. Just as in the theory of ordinary differential equations, matrix exponential functions also play a central rôle in the theory of certain types of differential equations for matrix-valued functions and these are important in many applications of Lie theory.
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© 2002 Springer-Verlag London
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Baker, A. (2002). Exponentials, Differential Equations and One-parameter Subgroups. In: Matrix Groups. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0183-3_2
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DOI: https://doi.org/10.1007/978-1-4471-0183-3_2
Publisher Name: Springer, London
Print ISBN: 978-1-85233-470-3
Online ISBN: 978-1-4471-0183-3
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