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May
29
awarded  Citizen Patrol
Mar
16
comment Any continuous group homomorphism from $\mathbb{R}$ to $GL(n,\mathbb{C})$
It need not. eg if $X=1$ it will not be. Hint: Take $X=\phi(1)$ and use that $\phi$ is a group homomorphism to extend to $\mathbb{Z}$ and then to $\mathbb{Q}$.