Results 1 to 2 of 2

Math Help - [SOLVED] How can U + W be S-invariant even if U and W aren't?

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    4

    [SOLVED] How can U + W be S-invariant even if U and W aren't?

    I don't understand how if U and W are subspaces of V such that S\left ( \vec{u} \right ) \epsilon W,\forall \vec{u}\epsilon U and S\left ( \vec{w} \right ) \epsilon U,\forall \vec{w}\epsilon W then U + W will be S-invariant even if U and W aren't. Can someone explain this to me? I need to understand this to make an operator S for 2x2 matrices.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    Well if u+w \in U+W, then S(u+w)=S(u)+S(w) \in W+U = U+W.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving that there aren't any more homomorphisms
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 23rd 2011, 06:51 PM
  2. Replies: 1
    Last Post: June 13th 2011, 09:40 AM
  3. Show the limit of two composite functions aren't =
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 20th 2009, 05:42 PM
  4. Integrals aren't real...
    Posted in the Calculus Forum
    Replies: 13
    Last Post: April 29th 2009, 11:46 AM

Search Tags


/mathhelpforum @mathhelpforum