i know this method but it's not working very well , there is a clear method by Dr. frederic P. sculler, using push-forward of left invariant vector field in a chart , but the issue is that i can not project the matrix of ( SO(3) group ) in a proper way on a chart . can i do this method for a one...
hello every one
can one please construct for me left invariant vector field of so(3) rotational algebra using Euler angles ( coordinates ) by using the push-forward of left invariant vector field ? iv'e been searching for a method for over a month , but i did not find any well defined method...
my friend Rocky Marciano , I'm working on this method for SO(2) , SU(2) ,SO(3) AND SO(3,1) . i found all the lie algebras of each manifold by approximation method , states that there exists a small parameter (e)[(infinitesimal change)] in R^1 close to the Identity of the gruop (e.g. ) G Such...
The details are all in that video , the problem is that i can't find a single parameterization such that there exists some slots in the matrix ( e.g. SO(3) ) such that the parameters lying in each slot are independent of each other , the euler angles parameterization of SO(3) gives rise that...
hello every one .
can someone please find the left invariant vector fields or the generator of SO(2) using Dr. Frederic P. Schuller method ( push-forward,composition of maps and other stuff)
Dr Frederic found the left invariant vector fields of SL(2,C) and then translated them to the identity...
Hello every one .
first of all consider the 2-dim. topological manifold case
My Question : is there any difference between
$$f \times g : R \times R \to R \times R$$
$$(x,y) \to (f(x),g(y))$$
and $$F : R^2 \to R^2$$
$$(x,y) \to (f(x,y),g(x,y))$$
Consider two topological...