If we seek a bijection $$\wedge^p V \to \wedge^{n-p} V$$ for some inner product space ##V##, we might think of starting with the unit ##n##-vector and removing dimensions associated with the original vector in ##\wedge^p V ##. Might this be expressed as a sequence of steps by some binary function ##G##,(adsbygoogle = window.adsbygoogle || []).push({});

$$\star \left( \mathbf{x} \wedge \mathbf{y} \right) = G\Big(\mathbf{x}, G\big( \mathbf{y}, \mathbf{e}_1 \wedge \dots \wedge \mathbf{e}_n\big)\Big) $$

in which case how might we express ##G##?

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# A Hodge Dual as Sequence of Grade Reducing Steps

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