V članku pokažemo, da je Liejeva algebra ▫$\mathcal{L}$▫ vseh poševno simetričnih matrik glede na transponiranje ali glede na simplektično involucijo določena z ničelnim produktom. Torej je vsaka ...bilinearna preslikava ▫$\{\cdot ,\cdot\}$▫ iz ▫$\mathcal{L} \times \mathcal{L}$▫ v vektorski prostor ▫$X$▫, ki zadošča pogoju ▫$\{x, y\} = 0$▫ za vsaka ▫$x,y \in {\mathcal L}$▫ z lastnostjo ▫$[x, y] = 0$▫, oblike ▫$\{x,y\} = T ([x, y])$▫, kjer je ▫$T$▫ linearna preslikava.
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