# Transversion

$$\mathfrak T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{423} + \dfrac{\tau_y}{2} \mathbf e_{431} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{412} + \large\unicode{x1d7d9}}$$ .
When a transversion $$\mathfrak T$$ is applied to a round point, it is equivalent to premultiplying the point by the $$5 \times 5$$ matrix
$$\begin{bmatrix} 1 & 0 & 0 & 0 & -\tau_x \\ 0 & 1 & 0 & 0 & -\tau_y \\ 0 & 0 & 1 & 0 & -\tau_z \\ -\tau_x & -\tau_y & -\tau_z & 1 & \dfrac{\tau^2}{2} \\ 0 & 0 & 0 & 0 & 1 \end{bmatrix}$$ .