 Symplectic basis

A symplectic basis $(e_1,\dots ,e_n,f_1,\dots ,f_n)$ has pairings $\omega (e_i,f_j)={\delta }_{ij}$ and all pairings between two $e_i$ or two $f_i$ equal to zero.

A symplectic basis is a particular type of basis for a symplectic vector space, which is a vector space equipped with a non-degenerate, skew-symmetric bilinear form known as the symplectic form.