Contractions of indices of the 4-vectors

[nikol]

Hi, can someone confirm those or did I not get the meaning of the 4-vectors indices:

$\partial^{\mu}x_{\mu}=4;\partial^{\mu}x^{\mu}=2;\partial^{\mu}x_{\nu}= \delta ^{\mu}_{\nu};\partial^{\mu}x^{\nu}=g^{\mu\nu}$

 

[Chopin]

Those are all numerically correct, however the second one is not a valid tensor equation, because you have two raised $\mu$ indices. Correct tensor equations always have contractions between one upper and one lower index--if you don't do that, the resulting equation is not Lorentz-invariant.

 

[nikol]

Thank you for the clarification