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I Covariant and contravariat components

  1. Jul 11, 2016 #1
    hi, Initially I would like to ask a little and basic question: I know that $$v=\sum_{i=0} e_i v^i$$ where $$v^i=e^i v$$ But sometimes I think we can write the first equation like $$v=\sum_{i=0} e_i e^i v$$, and I am aware that $$e_i e^i=1$$ , then our equation becomes $$v=\sum_{i=0} v$$, ın short if we take the sum over i at the end, our equation becomes v=3v or v=5v.......Could you help me get over this confusion I have sometimes in my mind??? Very thanks in advance....
  2. jcsd
  3. Jul 11, 2016 #2


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    You really should start writing out your inner products or you will keep making mistakes like this. What appears in your third sum is not ##(\vec e_i \cdot \vec e^i)\vec v##, it is ##\vec e_i (\vec e^i \cdot \vec v)##.
  4. Jul 12, 2016 #3
    ok I got it I managed to ensure the derivation myself. Thanks....
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