Results 1 to 2 of 2

Math Help - iso to the circle group

  1. #1
    ux0
    ux0 is offline
    Junior Member
    Joined
    Oct 2009
    Posts
    58

    iso to the circle group

    I need to prove that the special orthogonal group SO(2,\mathbb{R}) is isomorphic to the circle group S^1.

    I was considering using the case in which

    \varphi :A= \begin{bmatrix}<br />
 cos \alpha & -sin \alpha \\ <br />
 sin \alpha & cos \alpha<br />
\end{bmatrix} \mapsto (cos \alpha, sin \alpha)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by ux0 View Post
    I need to prove that the special orthogonal group SO(2,\mathbb{R}) is isomorphic to the circle group S^1.

    I was considering using the case in which

    \varphi :A= \begin{bmatrix}<br />
cos \alpha & -sin \alpha \\ <br />
sin \alpha & cos \alpha<br />
\end{bmatrix} \mapsto (cos \alpha, sin \alpha)

    As simple as that.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Order of Group. Direct Product of Cyclic Group
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: November 19th 2011, 01:06 PM
  2. Replies: 1
    Last Post: November 4th 2009, 09:52 AM
  3. Quick questions on Group Theory - Cosets / Normal Group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 16th 2009, 08:39 AM
  4. Fundamental group of the circle S^1
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 19th 2009, 04:55 PM
  5. Group Theory Question, Dihedral Group
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2008, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum