Results 1 to 2 of 2

Math Help - For any two subspaces of an inner product space..

  1. #1
    Junior Member
    Joined
    Oct 2012
    From
    Ohio
    Posts
    48

    For any two subspaces of an inner product space..

    Prove that for any two subspaces W1 and W2 of an inner product space V, we have

    a) (W1 + W2)^⊥ = W1^⊥ ∩ W2^⊥ and

    b) (W1 ∩ W2)^⊥ = W1^⊥ + W2^⊥

    Hint: The second follows from the first- you may use the fact that (W^⊥)^⊥ = W.

    Any help would be greatly appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,837
    Thanks
    676

    Re: For any two subspaces of an inner product space..

    Hey TimsBobby2.

    Hint: The perpendicular space of W1 + W2 will not include anything that spans along that space (figure out the plane that spans the two spaces and get the perpendicular space of that).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: August 16th 2011, 02:52 PM
  2. linear space and subspaces
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 19th 2010, 12:44 PM
  3. Subspaces of polynomial vector space
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 13th 2010, 08:40 AM
  4. Geodesic space and subspaces
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 3rd 2010, 04:45 AM
  5. Replies: 3
    Last Post: April 23rd 2009, 11:59 PM

Search Tags


/mathhelpforum @mathhelpforum