Symplectic vector space

A symplectic vector space $(𝑉, 𝜔)$ over $𝕂$ is a vector space over $𝕂$ equipped with a symplectic form $𝜔$ , #m/def/geoalg this being an alternating nondegenerate bilinear form $𝜔 : 𝑉 \times 𝑉 \to 𝕂$ , meaning for all $𝑣 \in 𝑉$

𝜔 (𝑣, 𝑣) = 0 𝜔 (𝑣, 𝑉) = 0 ⟺ 𝑣 = 0

Examples

The determinant form on $𝕂 2$ .
More generally, the standard symplectic space.

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