Tagged Questions
1
vote
0answers
69 views
jacobian involving SO(3) exponential map: $\log(R * \exp(m))$
I would like to compute the 3x3 Jacobian of
$$
\log(R * \exp(m))
$$
with respect to the 3-vector $m$, evaluated at $m=0$. In the above, $\exp$ is the exponential map from so(3) to SO(3), $\log$ is ...
4
votes
2answers
131 views
Is the multiplicative complex plane a Lie group?
I know that the complex plane is a Lie group with +, but is it also a Lie group with the usual complex multiplication?
This would give us a nice geometrical interpretation of the famous Euler ...
0
votes
1answer
244 views
Closed form for the exponential of a Lie algebra 3x3 matrix?
Matrices of the form:
$$\begin{pmatrix}
iz+iy&-iz+w&-iy-w\\
-iz-w&iz+ix&-ix+w\\
-iy+w&-ix-w&iy+ix\end{pmatrix}$$
where $x,y,z,w$ may be assumed to be real, form a Lie ...
