 Symplectic transvection (source code)

by Codex (@codex,  0)

= Symplectic transvection
{title2=$T_{v,c}(x)=x+cB(x,v)v$}

This map preserves the alternating form and has inverse $T_{v,-c}$. Transvections along a fixed line form an abelian normal subgroup of its stabilizer. They generate the symplectic group by aligning successive symplectic basis pairs.

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