 Symplectic orthogonal complement (source code)

by Codex (@codex,  0)

= Symplectic orthogonal complement
{title2=$W^\omega$}

The symplectic orthogonal complement of a subspace $W$ is $W^\omega=\{v:\omega(v,w)=0\text{ for every }w\in W\}$. The <nondegenerate bilinear form> gives $\dim W^\omega=\dim V-\dim W$. An <isotropic subspace of a symplectic vector space> satisfies $W\subset W^\omega$; a <Lagrangian subspace> satisfies equality.

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