Abstract
The exponential of a matrix plays a crucial role in the theory of Lie groups. The exponential enters into the definition of the Lie algebra of a matrix Lie group (Sect. 3.3) and is the mechanism for passing information from the Lie algebra to the Lie group.
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Hall, B. (2015). The Matrix Exponential. In: Lie Groups, Lie Algebras, and Representations. Graduate Texts in Mathematics, vol 222. Springer, Cham. https://doi.org/10.1007/978-3-319-13467-3_2
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