A non-zero alternating tensor w splits the bases of V into two disjoint groups, those with [itex]\omega(v_1,\cdots,v_n)>0[/itex] and those for which [itex]\omega(v_1,\cdots,v_n)<0[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

So when we speak of the orientation of a vector space, we need to say the orientation with respect to a certain tensor, correct?

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# Orientation of a vector space

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