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In linear algebra, a standard symplectic basis is a basis e i , f i {\displaystyle {\mathbf {e} }_{i},{\mathbf {f} }_{i}} of a symplectic vector space, which is a vector space with a nondegenerate alternating bilinear form ω {\displaystyle \omega } , such that ω = 0 = ω , ω = δ i j {\displaystyle \omega =0=\omega ,\omega =\delta _{ij}}. A symplectic basis of a symplectic vector space always exists; it can be constructed by a procedure similar to the Gram–Schmidt process. The existence of the basis implies in particular that the dimension of a symplectic vector space is even if it is finite.