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Sep 15 at 10:58 comment added akr If we define W as the skew-symmetric tensor and w as the axial vector, such that for a vector v, the relationship W v = w × v holds, the correct answers to get the axial vector of the skew-symmetric matrix are: w = Normal@HodgeDual[Transpose[W]] and w= Normal@HodgeDual[-W]. A negative sign is missing in the above answer, if you are seeking w based on W v = w × v.
Oct 23, 2014 at 23:44 comment added evanb ... of course there's a built-in. Should have known.
Oct 23, 2014 at 23:41 history edited Mr.Wizard CC BY-SA 3.0
added 60 characters in body
Oct 23, 2014 at 22:47 history answered ybeltukov CC BY-SA 3.0