Minkowski metric and Minkowski space
with : a bilinear symmetric inner product on that is not positive definite.
Definition 4.33 (Minkowski Metric and Minkowski Space)
The inner product defined by
where is called the Minkowski metric.
equipped with the Minkowski metric is called a Minkowski space.
Matrices preserving the metric
With the standard basis vectors satisfying , and , a linear map represented by preserves the Minkowski metric exactly when
by comparing with . Taking determinants gives , so such matrices have , and they form a group.
Related
Stated in
- Definition 4.33 (Minkowski Metric and Minkowski Space)§4.9.2 2D Minkowski Space and Lorentz Transformations