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\mathb{L} : \mathcal{S} \mapsto \mathcal{S'}
\mathb{L}
\mathb{L} = \begin{pmatrix} a & b \\ d & e \end{pmatrix}
\mathb{L} = \begin{pmatrix} \gamma & b \\ b & \gamma \end{pmatrix}
\mathb{L} = \begin{pmatrix} \gamma & \frac{-v}{c} \gamma \\ \frac{-v}{c} \gamma & \gamma \end{pmatrix}
\mathb{L}\mathb{L}^{-1} = \begin{pmatrix} \gamma & \frac{-v}{c} \gamma \\ \frac{-v}{c} \gamma & \gamma \end{pmatrix}\begin{pmatrix} \gamma & \frac{v}{c} \gamma \\ \frac{v}{c} \gamma & \gamma \end{pmatrix}= \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}
\displaystyle = v \gamma m_0 v \right\ + c^2 m_0 \sqrt{1-v^2/c^2} -m_0 c^2
\displaystyle = \gamma (m_0 v^2 \right\ + c^2 m_0 (1-v^2/c^2)) -m_0 c^2
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