Hey PF!(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to understand what is meant when we say a vector is invariant, which I believe is independent of a coordinate system. I have already read a PF post here: https://www.physicsforums.com/showthread.php?t=651863.

I'm looking at DH's post, and this makes a lot of sense!

However, I have read the following, which I am trying to interpret. Please read this and help me out, if you can:

Consider the single point velocity stress tensor, ##v_i v_j## where ##v_i## is the ##i##th component of velocity. First rotate the coordinate system 90 degrees around the ##x_1## axis so the old ##x_3## axis becomes the new ##x′_2## axis and the old negative ##x_2## axis becomes the new ##x′_3## axis. It is easy to see ##v′_2 v′_3## in the new coordinate system must be equal to ##-v_2 v_3## in the old. But isotropy [don't worry about interpreting this] requires that the form of ##v_i v_j## be independent of coordinate system. This clearly is possible only if ##v_2 v_3 = 0##.

Thanks!!

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# Invariant Vectors

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