Symplectic linear map
= Symplectic linear map
{title2=$A^*\omega_W=\omega_V$}
A <linear map> $A:(V,\omega_V)\to(W,\omega_W)$ is symplectic when it pulls back the target <symplectic form> to the source form. <Nondegenerate bilinear form> makes such a map <injective>. In equal finite dimensions it is an <isomorphism>. The automorphisms form the <symplectic group> and preserve the <symplectic orientation> on the ambient space and on every <symplectic subspace>.