In linear algebra, a standard symplectic basis is a basis of a symplectic vector space, which is a vector space with a nondegenerate alternating bilinear form , such that . A symplectic basis of a symplectic vector space always exists; it can be constructed by a procedure similar to the Gram–Schmidt process.[1] The existence of the basis implies in particular that the dimension of a symplectic vector space is even if it is finite.

See also

Notes

  1. Maurice de Gosson: Symplectic Geometry and Quantum Mechanics (2006), p.7 and pp. 12–13

References

  • da Silva, A.C., Lectures on Symplectic Geometry, Springer (2001). ISBN 3-540-42195-5.
  • Maurice de Gosson: Symplectic Geometry and Quantum Mechanics (2006) Birkhäuser Verlag, Basel ISBN 978-3-7643-7574-4.
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