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Gram-Schmidt Question

  1. Dec 31, 2009 #1
    1. The problem statement, all variables and given/known data
    First off, this isn't for a class, I'm just going over some material, however this does come from a textbook, so I figure this is a reasonable place to ask the question! Here's the question:

    Use the Gram-Schmidt procedure to orthogonalize the following vectors:


    2. Relevant equations
    Let's not even worry about v3 right now. Let's just orthogonalize v1 and v2.

    3. The attempt at a solution
    First off, we let v1=u1 = [(1+i),1,i]

    Now, we can find u2 by: [tex]u2 = v2 - \frac{<u1,v2>}{||u1||^2}u1[/tex]

    The norm of u1 is 2, therefore squaring that we get 4.
    When I took <u1,v2> I got 4. Therefore 4/4 = 1.
    This leaves us with u2 = v2 - u1 = (-1,2,1-i)
    HOWEVER, u2 dot u1 = 2
    and of course if they were orthogonal they should equal 0.
    Not sure where I made a mistake... so if anyone can help that would be appreciated!


  2. jcsd
  3. Dec 31, 2009 #2


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    (-1,2,1-i) dot ((1+i),1,i) is equal to zero. Not 2. I think you forgot a complex conjugate when you did the inner product.
  4. Dec 31, 2009 #3
    Yes, indeed...
    my mind has been meandering around Hilbert space too long ;)
  5. Dec 31, 2009 #4


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    Maybe you can be my tour guide :rofl:
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