Eric Lengyel: Created page with "NOTOC A ''transversion'' is a reciprocal transformation performed by the operator :$$\mathfrak T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{423} + \dfrac{\tau_y}{2} \mathbf e_{431} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{412} + \large\unicode{x1d7d9}}$$ . == Matrix Form == 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..."

2023-08-06T03:20:25Z

Created page with "__NOTOC__ A ''transversion'' is a reciprocal transformation performed by the operator :$$\mathfrak T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{423} + \dfrac{\tau_y}{2} \mathbf e_{431} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{412} + \large\unicode{x1d7d9}}$$ . == Matrix Form == 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..."

New page

__NOTOC__
A ''transversion'' is a reciprocal transformation performed by the operator

:$$\mathfrak T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{423} + \dfrac{\tau_y}{2} \mathbf e_{431} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{412} + \large\unicode{x1d7d9}}$$ .

== Matrix Form ==

When a transversion $$\mathfrak T$$ is applied to a [[round point]], it is equivalent to premultiplying the point by the $$5 \times 5$$ matrix

:$$\begin{bmatrix}
1 & 0 & 0 & 0 & -\tau_x \\
0 & 1 & 0 & 0 & -\tau_y \\
0 & 0 & 1 & 0 & -\tau_z \\
-\tau_x & -\tau_y & -\tau_z & 1 & \dfrac{\tau^2}{2} \\
0 & 0 & 0 & 0 & 1
\end{bmatrix}$$ .

== See Also ==

* [[Translation]]
* [[Rotation]]
* [[Dilation]]

Transversion - Revision history