i have two questions. First one is: am i correct in thinking that a line vector subspace of $\Bbb R^2$ is rotation invariant if $\theta = \pi$ or $2\pi$? Second, i am told that there is a non trivial rotation invariant subspace of $\Bbb C^2$ for $\theta = \pi/2$ but i am having trouble visualizing it (considering a rectangle or circle is not a space how could this happen?)
Thanks in advance