# Four-vector

A four-vector is a four element vector that is a rank 1 class tensor in that its element notation expression carries 1 index and it transforms according to a tensor transformation. For example a four vector expressed as a contravariant rank 1 tensor ${\displaystyle T^{\mu }}$ transforms according to

 ${\displaystyle T'^{\mu }={\frac {\partial x'^{\mu }}{\partial x^{\nu }}}T^{\nu }}$

and the four vector expressed as a covariant rank 1 tensor ${\displaystyle T_{\mu }}$ transforms according to

 ${\displaystyle T'_{\mu }={\frac {\partial x^{\nu }}{\partial x'^{\mu }}}T_{\nu }}$