Minkowski space is a four-dimensional space possessing a Minkowski metric, i.e., a metric tensor having the form
 |
Alternatively (though less desirably), Minkowski space can be considered to have a Euclidean metric with imaginary time coordinate 
where 
is the speed of light (by convention 
is normally used) and where i
is the imaginary number 
. Minkowski space unifies three-dimensional Euclidean space plus time (the "fourth dimension")
in Einstein's theory of special relativity.
In the equation above, the metric signature is 
in the convention that reports the number of positive
squares first, or 
in the convention that reports the number of negative
squares first. Minkowski space is correspondingly denoted 
or 
. Reordering the squared terms does not change the metric signature within either convention.
The Minkowski metric induces a four-dimensional Lorentzian inner product (sometimes referred to as the Minkowski inner product), which fails to be positive definite (Ratcliffe 2006).
