Examples
The basic example is the squeeze mappings, which is the group SO+(1,1) of (the identity component of) linear transforms preserving the unit hyperbola. Concretely, these are the matrices and can be interpreted as hyperbolic rotations, just as the group SO(2) can be interpreted as circular rotations. In physics, the Lorentz group O(1,3) is of central importance, being the setting for electromagnetism and special relativity.
Read more about this topic: Indefinite Orthogonal Group
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