Results 1 to 3 of 3

Math Help - products

  1. #1
    Super Member
    Joined
    Aug 2009
    Posts
    639

    products

    does reflections in any axis passing the origin and rotation commute?

    i think they do commute and hence the group structure of both tgt should be a direct product but am not sure why indirect products are used in symmetries?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    They do not commute. Draw a square, label the vertices, and try it out. Dihedral groups are not abelian.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member HappyJoe's Avatar
    Joined
    Sep 2010
    From
    Denmark
    Posts
    234
    Rotations and reflections do not generally commute.

    For example, consider reflection in the x-axis in R^2, and counterclockwise rotation by 90 degrees. Then the vector (0,1) ends up in (1,0) upon reflection and then rotation, while it ends up in (-1,0) upon rotation and then reflection.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Dot products
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 1st 2011, 03:32 PM
  2. Inner Products
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 28th 2011, 05:40 PM
  3. ...norm takes products to products.
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 23rd 2010, 08:55 PM
  4. Inner Products
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: April 17th 2010, 08:34 PM
  5. Inner products
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 4th 2007, 07:36 PM

Search Tags


/mathhelpforum @mathhelpforum