A spacelike four-vector 
has squared Lorentzian length
, using the convention in
which the time coordinate has negative squared length.
The square of the four-vector norm is the quadratic form associated with
the Lorentzian inner product 
on 
-dimensional Lorentzian
space with 
and metric signature 
in the negative-first convention. In this more general
environment, the Lorentzian inner product
of two vectors 
and 
has the form
 |
whereby one defines a vector 
to be spacelike precisely when 
.
Geometrically, the collection of all spacelike vectors lies in the open set of 
formed by the exterior of the light
cone.
