I'm wondering why [itex]1/k![/itex] is needed in Alt(T), which is defined as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{1}{k!}\sum_{\sigma \in S_k} \mbox{sgn}\sigma T(v_{\sigma(1)},\cdots,v_{\sigma(k)})[/tex]

After removing [itex]1/k![/itex], the new [itex]\mbox{Alt}[/itex], [itex]\overline{\mbox{Alt}}[/itex], still satisfies [itex]\overline{\mbox{Alt}}(T)(v_1,\cdots,v_i,\cdots,v_j,\cdots,v_k)=-\overline{\mbox{Alt}}(T)(v_1,\cdots,v_j,\cdots,v_i,\cdots,v_k)[/itex], which means [itex]\overline{\mbox{Alt}}[/itex] is an alternating tensor

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# The mapping to alternating tensors

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