Results 1 to 2 of 2

Math Help - Orthonormal vectors

  1. #1
    pkr
    pkr is offline
    Junior Member
    Joined
    Nov 2008
    Posts
    49

    Orthonormal vectors



    Really stuck on this, I know that two vectors are orthogonal if their inner product space is 0, and the're orthonormal if they have norm 1, but i'm really not sure how to go about this question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,421
    Thanks
    1856
    Quote Originally Posted by pkr View Post


    Really stuck on this, I know that two vectors are orthogonal if their inner product space is 0, and the're orthonormal if they have norm 1, but i'm really not sure how to go about this question.
    Hopefully, you also know some basic properties of the inner product:
    <u+ v, w>= <u,w>+ <v,w>
    <au, v>= a<u, v>
    and
    <u, v>= \overline{<v, u>}
    if the vector space is over the complex numbers (the overline is the complex conjugate).

    Using those, <av_1+ bv_2, cv_1+ dv_2>= <av_1,cv_1+ dv_2>+ <bv_2,cv_1+ dv_2> = <av_1,cv_1>+ <av_1,dv_2>+ <bv_2,cv_1>+ <bv_2, cv_1> = a\overline{c}<v_1,v_1>+ a\overline{d}<v_1,v_2>+ b\overline{c}<v_2,v_1>+ b\overline{d}<v_2,v_1> and now you can use the fact that v_1 and v_2 are orthonormal.

    Apply that to your problem. Tedious but straightforward.

    (I just re-read the problem and noticed that the set of "v" vectors in the definition of w1 and w2 are disjoint! Gosh this problem is trivial!)
    Last edited by HallsofIvy; May 13th 2009 at 08:37 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orthonormal Set
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 2nd 2011, 03:07 AM
  2. Change these 2 vectors into an orthonormal set
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 27th 2010, 04:51 PM
  3. Orthonormal and orthogonal vectors
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 17th 2010, 08:04 PM
  4. [URGENT] Strange Orthonormal Vectors Problem
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 16th 2009, 10:31 AM
  5. Urgent homework help!! Orthonormal vectors?
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 13th 2008, 10:40 AM

Search Tags


/mathhelpforum @mathhelpforum