Retrieving "Coordinate Transformation" from the archives

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1. Angular Momentum Tensor

   Linked via "coordinate changes"

   | Spatial Rotation $\mathcal{R}$ | $\mathcal{R}^{-1} \mathcal{L}{ij} \mathcal{R} = \mathcal{L}'{ij}$ | $\mathcal{R}^{-1} \mathcal{L}{0i} \mathcal{R} = \mathcal{L}'{0i}$ |
   | Spatial Boost $\mathcal{B}$ | $\mathcal{B}^{-1} \mathcal{L}{ij} \mathcal{B} = \mathcal{L}'{ij}$ | $\mathcal{B}^{-1} \mathcal{L}{0i} \mathcal{B} = \mathcal{L}'{0i} + \text{Terms involving } T_{0j}$ |
   | Transformation Property | Transforms as a rank-2 tensor density under coordinate changes. | Transforms as a tensor, exhibiting mixed covariance under [boosts](/entries/lorentz-bo…