Results 1 to 2 of 2

Math Help - more Adjoint of Linear operator confusion...

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    104

    more Adjoint of Linear operator confusion...

    So I have to prove the following, and not sure where to go with it:
    Prove that if V=W\oplus W^{\perp} and T is the projection on W along W^{\perp} then T=T*.
    Any help? THanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by dannyboycurtis View Post
    So I have to prove the following, and not sure where to go with it:
    Prove that if V=W\oplus W^{\perp} and T is the projection on W along W^{\perp} then T=T*.
    Any help? THanks
    let v_1=w_1+w_1', \ v_2=w_2+w_2' where w_i \in W, \ w_i' \in W^{\perp}. then <Tv_1,v_2>=<w_1,w_2+w_2'>=<w_1,w_2> and <v_1,Tv_2>=<w_1+w_1',w_2>=<w_1,w_2>.

    so <Tv_1,v_2>=<v_1,Tv_2> and thus T=T^*.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the adjoint of a linear operator
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: November 19th 2011, 08:12 PM
  2. Adjoint of linear Operator
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 16th 2011, 07:27 AM
  3. self-adjoint linear operator
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 23rd 2011, 01:32 AM
  4. Replies: 2
    Last Post: December 5th 2009, 02:30 AM
  5. Normal, self-adjoint, or neither linear operator
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 15th 2008, 12:04 PM

Search Tags


/mathhelpforum @mathhelpforum