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Gram-Schmidt Process

  1. Dec 15, 2007 #1
    1. The problem statement, all variables and given/known data

    V = span(S) where S = {(1, i, 0), ((1-i), 2, 4i)}, and x = ((3+i), 4i, -4)

    Obtain the orthogonal basis, then normalize for the orthonormal basis, and then compute the fourier coefficients.
    2. Relevant equations

    v2 = w2 - (<w2,v1>)(v1)/(||v1||²)

    3. The attempt at a solution

    So using this above equation, I get ||v1||² to equal zero because 1 + i² = 1 - 1 = 0, thus I'm dividing by zero, so where do I go from here, or am I miscalculating somewhere?
     
  2. jcsd
  3. Dec 15, 2007 #2

    robphy

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    How do you compute the square-norm of a complex number?
     
  4. Nov 30, 2008 #3
    Ok this is what you did wrong:

    ||v1||² = v1* . v1 = (1, i, 0)*. (1, i, 0) = 1+(-i)(i)=1+1=2
     
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