A vector space$V$ over a field $k$ is symplectic if it is equipped with an exterior 2-form$\omega \in \Lambda^2_k V$ such that $\omega^{\wedge n}=\omega\wedge\omega\wedge\cdots\wedge\omega$ has the maximal rank.

A subspace $W\subset V$ in a symplectic vector space is isotropic if $\omega(v,v) = 0$ for all $v\in W$ and Lagrangean (or lagrangian) if it is maximal isotropic (not proper subspace in any isotropic subspace). See wikipedia.