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[itex] \mathfrak{so}(p,q) = \Biggl\{ \left( \begin{array}{cc} X & Z \\ Z^t & Y \end{array} \right) \vline X \in M_p ( \mathbb{R} ), Y \in M_q ( \mathbb{R} ), Z \in M_{p \times q} ( \mathbb{R} ), X^t=-X, Y^t=-Y \Biggr\}[/itex]

i'm not really getting anywhere so any help is appreciated. thanks.