The Symplectic space reference article from the English Wikipedia on 24-Jul-2004
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Symplectic space

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You may wish to look at Symplectic manifold.

A symplectic space is a vector space equipped with a bilinear a nondegenerate, skew-symmetric, bilinear form. If of finite dimension, its dimension is necessarily even.

These spaces usually arise in the context of Symplectic groups.

This page is a stub that needs expanding, though its content is not really a subset of that of the Symplectic manifold page.