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Oct 24, 2017 at 10:42 history edited Ben McKay CC BY-SA 3.0
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Jul 13, 2017 at 8:06 comment added Chengbo Ben Mckay and J.c., thank you! I think that I will be able to work out the problem.
Jul 12, 2017 at 15:08 comment added j.c. I was about to give an answer based on this reference too; the relevant bit is Theorem 2.5. Most relevant to OP's question are the expressions in Eqs. 2.22a and 2.22b which show that invertibility of $C$ follows from the fact that $\Omega$, being symplectic on $P$, is nondegenerate and also nondegenerate on $S$.
Jul 12, 2017 at 14:53 history answered Ben McKay CC BY-SA 3.0