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Symplectic vector space

A symplectic vector space is a vector space equipped with a nondegenerate antisymmetric bilinear form. Every finite-dimensional symplectic vector space has even dimension: splitting off one symplectic two-plane leaves a smaller nondegenerate antisymmetric space, and induction completes the decomposition.

Ancestors (7)

  1. Nondegenerate bilinear form
  2. Bilinear form
  3. Linear algebra
  4. Algebra
  5. Area of mathematics
  6. Mathematics
  7. Home

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