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# Lie algebra of a matrix Lie group

| 🗖 nosplit | ↑ parent "Matrix Lie group" | words: 81
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For this sub-case, we can define the Lie algebra of a Lie group as the set of all matrices such that for all : $$etM∈G (129)$$
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TODO example it can also be seen that the Lie algebra is not closed under the group operation (matrix multiplication), but it is closed under the Lie bracket operation.
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