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\eta_{\alpha\beta} = \begin{pmatrix}[br]-c^2 & 0 & 0 & 0\\[br]0 & 1 & 0 & 0\\[br]0 & 0 & 1 & 0\\[br]0 & 0 & 0 & 1[br]\end{pmatrix}
\eta^{\alpha\beta} = \begin{pmatrix}[br]-1/c^2 & 0 & 0 & 0\\[br]0 & 1 & 0 & 0\\[br]0 & 0 & 1 & 0\\[br]0 & 0 & 0 & 1[br]\end{pmatrix}
\Lambda^{\mu'}{}_\nu = \begin{pmatrix}[br]\gamma & -\beta\gamma/c & 0 & 0\\[br]-\beta\gamma c & \gamma & 0 & 0\\[br]0 & 0 & 1 & 0\\[br]0 & 0 & 0 & 1[br]\end{pmatrix}
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