[Math] Get Transformation Matrix from M*v = v'?

Hi,
I want to dynamically generate a transformation matrix out of two given vectors.
Given is this formula:
M*v = v',
where M is a 3x3-Matrix, and the vectors v and v' are given and contain x,y,z-coords.
Is it possible to solve this equation-system via an algorithm? I already read about the Gauß' algorithm but I don't know if that is suitable for this kind of equation system and if yes, how to insert the vector into the initial matrix.

 

Gaussian elimination would be useful for finding v if you had M and v'. It doesn't work in this situation.

The problem is that there would be many valid matrixes that solve that equation for given v and v' - not one single one. Unless you have at least a little information about the nature of M, you won't be able to find one single solution.

 

The transformation matrix is a rotation-matrix.

 

Do you know the origin of the rotation? (I'm fairly sure you need to).

 

The origin is (0,0,0).
To go more into detail:
I want to create a Portal-like gameplay which requires to transform both the momentum and the view of the player whenever he goes through a portal. Each portal has got a vector which points out of the portal
(

--->

)
Hope that makes it clear

 

Ah I get you.

Do your portals only have 4 possible directions (North/South/East/West)?

If so, then its fairly easy to rotate by 90 degrees about the vertical axis (without going as far as using matrices).

 

No, they also should go up and down...
Maybe it's also possible to do this without vectors.