Why $\text{GL}_2(\mathbb{C})$ is connected?
I know this question answered several times here, but I don't want to jump directly into a rigorous proof, rather I am looking for an intuitive view.
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The "intuitive view" is that the exponential map $\exp: \mathfrak{gl}(n, \mathbb{C}) \to GL(n, \mathbb{C})$ is surjective. – Dietrich Burde Nov 04 '19 at 19:34
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I am not aware of the domain set.Pls explain. – Nov 04 '19 at 19:48
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The domain set is the vector space of all square matrices of size $n$ (with Lie bracket $[A,B]=AB-BA$, but you don't need this for just an intuitive view). And $\exp(A)=1+A/1!+A^2/2!+\cdots$. – Dietrich Burde Nov 04 '19 at 19:50