Pokažemo, da je jordanska algebra $▫\mathcal{S}$▫ vseh simetričnih matrik glede na transponiranje ali glede na simplektično involucijo določena z ničelnim produktom. Torej za vsako bilinearno ...preslikavo ▫$\{\cdot ,\cdot\}$▫ iz ▫$\mathcal{S} \times \mathcal{S}$▫ v vektorski prostor ▫$X$▫, ki zadošča pogoju ▫$\{x,y\}=0$▫, kadarkoli je ▫$x \circ y = 0$▫, obstaja taka linearna preslikava ▫$T \colon \mathcal{S} \to X$▫, da je ▫$\{x,y\} = T(x \circ y)$▫ za vse ▫$x,y \in \mathcal{S}$▫ (tu je ▫$x \circ y = xy+yx$▫).
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