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by Ciro Santilli (@cirosantilli, 37)

Lie algebra of GL(n)

 ... Mathematics Area of mathematics Geometry Differential geometry Lie group Important Lie group
 0 By others on same topic  0 Discussions  Updated 2025-05-29  +Created 1970-01-01  See my version
Tags: Lie algebra of a matrix Lie group
Is the set of all n-by-y square matrices.
Because GL(n) is a Lie group we can use Section "Lie algebra of a matrix Lie group".
For every matrix x in the set of all n-by-y square matrices Mn​, ex has inverse e−x.
Note that this works even if x is not invertible, and therefore not in GL(n)!
Therefore, the Lie algebra of GL(n) is the entire Mn​.

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