Results 1 to 6 of 6

Math Help - Suppose V is an inner product..

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Toronto
    Posts
    19

    Suppose V is an inner product..

    Suppose V is an inner product sapce
    and T:V-->V
    Show that dim(Im(T)) = dim(Im(T*))
    Last edited by dave52; March 26th 2013 at 04:14 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: Suppose V is an inner product..

    You mean "Suppose V is an inner product space". Now, what is the definition of T*?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    Toronto
    Posts
    19

    Re: Suppose V is an inner product..

    T* satisfies the equation <T(v),w> = <v,T*(w)> for all v,w in V?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2013
    From
    Toronto
    Posts
    19

    Re: Suppose V is an inner product..

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: Suppose V is an inner product..

    Quote Originally Posted by dave52 View Post
    T* satisfies the equation <T(v),w> = <v,T*(w)> for all v,w in V?
    Good! Now choose a basis for Im(T), w_1, ... w_n, and let v_i= T^*(w_i). Can you show that v_1,... v_n is a basis for Im(T*)?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jan 2013
    From
    Toronto
    Posts
    19

    Re: Suppose V is an inner product..

    linear independent property: for all a1,....,an ∈ R if a1v1+.......+anvn = 0
    spanning property: for every x in Im(T*) such that x = a1v1+.....+anvn
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: March 2nd 2011, 12:36 AM
  2. suppose..
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 1st 2010, 04:41 PM
  3. Suppose that g(t)...
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 5th 2009, 01:27 PM
  4. Suppose that...
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 13th 2009, 01:10 PM

Search Tags


/mathhelpforum @mathhelpforum