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If we do symplectic linear algebra on a finite-dimensional vector space $V$, then what does $$\omega(v,w) \neq 0$$ or $$\omega(v,w) = 0$$ actually tell us about the vectors $v,w$? ($\omega$ is the skew-symmetric non-degenerate bilinear form) Afais, the first property tells us that they are linearly independent.

If anything is unclear, please let me know.

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  • $\begingroup$ I believe you are correct about the first property. As for the implications of the second I am not sure. $\endgroup$ – Chill2Macht Jan 16 '17 at 11:09

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