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Why is there two versions..for example, I got some matrices for the x axis rotation

This is for the X AXIS

enter image description here

the other one is for the x axis also, it is..

enter image description here

I think it could be from going counterclockwise and clockwise(right hand rule?) on the axis..im not sure because when I did that..i didn't get the right result

terry
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  • One is the transpose of the other. – Ali Caglayan Oct 20 '14 at 16:30
  • More to the point, one is the inverse of the other. They are opposite rotations (well, assuming $\theta_x=\theta$). Which one is “right” depends on context, which is missing here. Also, there are four dimensions – is this from relativity theory, or is it just some random four dimensional space? – Harald Hanche-Olsen Oct 20 '14 at 16:33
  • There is the additional complication that one can define active and passive transformations (which is always confusing for people). – Fabian Oct 20 '14 at 16:46
  • @HaraldHanche-Olsen I think the OP is referring to the representation of three dimensional points and their rotations and transformations with homogeneous coordinates/transformations. They allow rotations and transformations to all be represented by multiplication by one 4 x 4 matrix. I am familiar with them from their use in robotics and computer graphics. – joeA Oct 20 '14 at 16:58
  • @joeA Yes, that is not unlikely. – Harald Hanche-Olsen Oct 20 '14 at 17:02

1 Answers1

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There appear to be two conventions for representing points in $\mathbb{R}^3$ with homogeneous coordinates. Basically, $(x,y,z)$ can be represented as $\begin{bmatrix}x&y&z&1\end{bmatrix}$ or as $\begin{bmatrix}x&y&z&1\end{bmatrix}^T = \begin{bmatrix}x\\y\\z\\1\end{bmatrix}$. The different conventions will correspond to different representations of homogeneous transformations, with one $Rot_x$ being the transpose of the other, which, as @Alizter pointed out, is what you have above.

joeA
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