## Minkowski Space

A 4-D space with the Minkowski Metric. Alternatively, it can be considered to have a Euclidean Metric, but with its Vectors defined by

 (1)

where is the speed of light. The Metric is Diagonal with
 (2)

so
 (3)

Let be the Tensor for a Lorentz Transformation. Then
 (4)

 (5)

 (6)

The Necessary and Sufficient conditions for a metric to be equivalent to the Minkowski metric are that the Riemann Tensor vanishes everywhere ( ) and that at some point has three Positive and one Negative Eigenvalues.