0
votes
3answers
58 views

Does R' = R*R'*R^(-1) hold?

Given two 3D rotation matrices ($3\times 3$) $R$ and $R'$, does this equivalence hold?: $R' = R*R'*R^{-1}$ My intuition tells me so, but I can't find a formal proof for it. Thanks.
1
vote
1answer
182 views

Orthogonal procrustes problem using quaternions

Hello I'm trying solve orthogonal procrustes problem in 3d with a help of quaternions. Original problem is: For matrix $A$ find orthogonal matrix $Q$ that $$||A-Q||_F =\min_{\Omega \in SO(3)} ...
0
votes
1answer
140 views

How do I find the euler angles if I already have start and ending vector?

I have two orthonormal bases and I need to find the rotation angle over every axes to go from the first to the second one. These are my base vectors: $$ E_1 = \begin{bmatrix} -0.7969 & 0.1778 ...
5
votes
3answers
513 views

Freedoms of real orthogonal matrices

I was trying to figure out, how many degrees of freedoms a $n\times n$-orthogonal matrix posses.The easiest way to determine that seems to be the fact that the matrix exponential of an antisymmetric ...