nLab (co)isotropic subspaces - table

type of subspace $W$ of inner product space	condition on orthogonal space $W^\perp$
isotropic subspace	$W \subset W^\perp$
coisotropic subspace	$W^\perp \subset W$
Lagrangian subspace	$W = W^\perp$	(for symplectic form)
symplectic space	$W \cap W^\perp = \{0\}$	(for symplectic form)