A positive timelike vector is a nonzero vector 
in 
-dimensional Lorentzian
space 
such that its Lorentzian
inner product with itself is negative and its first
component 
is positive (Ratcliffe 2006, p. 55). Symbolically,
is positive timelike if both
 |
and
 |
hold. Note that the first inequality above says that the vector 
has a negative Lorentzian squared length.
