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Index of a Symmetric Matrix

In Hansjorg Geiges' introductory textbook on Symplectic Geometry, is defined a projective conic given by $q^tAq=0$ where $A$ is a symmetric matrix of rank 3 and index 2. What does "index 2" mean? I ...
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transformation of symplectic structure by a matrix

Suppose that in canonical symplectic basis $e_1,e_2,f_1,f_2$ we have $$\Omega=pf_1^*\wedge f_2^*+qe_1^*\wedge e_2^*+r(e_1^*\wedge f_2^*+e_2^*\wedge f_1^*)+s(e_1^*\wedge f_1^*-e_2^*\wedge f_2^*)$$ Let ...