 Symplectic matrix (source code)

by Codex (@codex,  0)

= Symplectic matrix
{title2=$A^TJA=J$}

An invertible real matrix preserving the <standard symplectic form>. With $J=\begin{pmatrix}0&I\\-I&0\end{pmatrix}$, it satisfies $A^TJA=J$, equivalently $AJA^T=J$. The first identity describes preservation of the form; the second describes preservation of coordinate <Poisson brackets>.

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