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Apr 14, 2016 at 20:35 comment added Sasha No (over $\mathbb{C}$ positivity makes no sense). The trick is to fix one isotropic space, say $A_0$, then the components are distinguished by the parity of the dimension of intersection with $A_0$.
Apr 14, 2016 at 20:33 comment added user42804 But how to tell which component it is in? for example can we check the positivity of the determinants?
Apr 14, 2016 at 20:29 history answered Sasha CC BY-SA 3.0