Definition of Symplectic Matrix

In Wikipedia and also MathPlanet an equal definition of a symplectic matrix is offered :

$$\left( \begin{array}{ccc} A & B \\ C & D \end{array} \right)$$

is symplectic if and also just if :

$$A^TD-C^TB=I, A^TC=C^TA, D^TB=B^TD$$

yet it appears incorrect, given that, as an example :

$$\left( \begin{array}{ccc} 0 & 0 & -1 & 1 \\ 0 & 0 & 0 & -1 \\ 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{array} \right)$$

is symplectic yet does not please the problems. Or have I combined every little thing up?

MODIFY : this is insane talk. That matrix isn't symplectic! (except the kind specified in Wikipedia or MathPlanet.

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2019-12-03 23:51:50
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