Let $G$ be a matrix Lie group. The identity component $G_0$ of $G$ is the set of $A\in G$ for which there exists a continuous path $\gamma:[0,1]\to G$ such that $\gamma(0) = I$ and $\gamma(1) = A$. Because connectedness and path-connectedness are equivalent, in this case, $G_0$ amounts to the connected component of $G$ that contains the identity matrix $I$.
Wikidata ID: Q5988368