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Mar 25, 2011 at 0:40 comment added Yemon Choi Just as an afterthought, a direct proof that U(n) is connected; diagonalize, and then join each eigenvalue to 1 by moving it round the unit circle.
Mar 25, 2011 at 0:20 comment added Hugo Chapdelaine Hi Neil, thanks a lot for your amazingly simple proof that $GL_n(\mathbf{C})$ is connected!
Mar 24, 2011 at 21:55 history answered Neil Strickland CC BY-SA 2.5