$GL(n)$, $GL(n,\mathbb{R})$, $GL(n,\mathbb{C})$
The general linear group consists of invertible matrices of rank $n$. It corresponds with the linear isomorphism of $\mathbb{R}^n$ into itself. Its Lie algebra is denoted by $\mathfrak{gl}(n)$, and is made of all matrices of order $n$ with the Lie bracket
$$ [A,B]=AB-BA $$________________________________________
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Author of the notes: Antonio J. Pan-Collantes
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