1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:

    v1=[(1+i),1,i]
    v2=[i,3,1]
    v3=[0,28,0]

    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!

    cheers,

    -astropi
     
  2. jcsd
  3. Dec 31, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    (-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 ;)
    Thanks!
     
  5. Dec 31, 2009 #4

    diazona

    User Avatar
    Homework Helper

    Maybe you can be my tour guide :rofl:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...