Connection between Lorentz group and rotation group
The rotation group can be thought of as \(3\times 3\) matrices \(R\) that satisfies \(I = R^{T}IR\), while the Lorentz group is \(\eta = \Lambda^{T}\eta\Lambda\), where \(I\) is the Euclidean metric and \(\eta\) is Lorentzian[1].
[1] Carroll Sean (2003). Spacetime and Geometry - an Introduction to General Relativity
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