I Covariant and contravariat components

1. Jul 11, 2016

mertcan

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. Jul 11, 2016

Orodruin

Staff Emeritus
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 $\vec e_i (\vec e^i \cdot \vec v)$.

3. Jul 12, 2016

mertcan

ok I got it I managed to ensure the derivation myself. Thanks....