# Symplectic basis

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

- ↑ 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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