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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Orientation of a vector space

**Physics Forums | Science Articles, Homework Help, Discussion**