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symplectic basis : ウィキペディア英語版
symplectic basis
In linear algebra, a standard symplectic basis is a basis _i, _i of a symplectic vector space, which is a vector space with a nondegenerate alternating bilinear form \omega, such that \omega(_i, _j) = 0 = \omega(_i, _j), \omega(_i, _j) = \delta_. A symplectic basis of a symplectic vector space always exists; it can be constructed by a procedure similar to the Gram–Schmidt process.〔Maurice de Gosson: ''Symplectic Geometry and Quantum Mechanics'' (2006), p.7 and pp. 12–13〕 The existence of the basis implies in particular that the dimension of a symplectic vector space is even if it is finite.
== See also ==

*Darboux theorem
*Symplectic frame bundle
*Symplectic spinor bundle
*Symplectic vector space

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