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

ω

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.

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