Minkowski-space/Observer vector/Definition

Let ${\displaystyle {}V}$ be a Minkowski space, endowed with a Minkowski form ${\displaystyle {}\left\langle -,-\right\rangle }$. A vector ${\displaystyle {}v\in V}$ fulfilling

${\displaystyle {}\left\langle v,v\right\rangle =-1\,}$

is called observer vector or four-velocity of an observer.