[[Commutator]]
# Linear commutator

The **linear commutator** is a particular example of a [[Commutator]].
Given two [[Linear endomorphism|linear endomorphisms]] $A,B \in \Vect_{\mathbb{K}}(V,V)$ the commutator is defined as #m/def/linalg 
$$
\begin{align*}
[A,B] = AB-BA
\end{align*}
$$
This defines a [[Lie algebra]] called [[General linear Lie algebra|$\opn{\mathfrak{gl}}V$]].

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#state/tidy | #lang/en | #SemBr