Hello!
Thank you very much for your detailed reply. I must admit that I'm pretty new to transformation matrices and have not yet entirely understood the mathematical meaning of eigenvalues and eigenvectors although I try hard to understand everything I can read about it, but with some help I surely learn a lot faster.
I'm rotating in a projective three-dimensional space, that's why I use a 4x4 matrix.
To give a more specific example, I have a transformation matrix that is the following:
\begin{bmatrix}0.893 & 0.060 & -0.447 & 20 \\ -0.157 & 0.97 & -0.184 & 15 \\ -0.423 & -0.235 & -0.875 & 45 \\ 0 & 0 & 0 & 1 \end{bmatrix}
This transformation matrix should transform the object with a translation of 20 15 45 and a rotation of -15 25 -10 (xyz).
Now the eigenvalues. I don't know if I've understood the meaning of them correctly, but if yes the eigenvalues for this matrix should be in the identity matrix which is:
\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}
So if I'm still on the right track, the eigenvectors, which are the axes of rotation, are simply
\left(1, 0, 0, 0) for x
\left(0, 1, 0, 0) for y
\left(0, 0, 1, 0) for z
Am I still on the right track or am I totally and fatally wrong?