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Homework Help: Orthonormal basis for subsets of C^3

  1. Mar 30, 2010 #1
    We want to find a basis for W and W_perpendicular for W=span({(i,0,1)}) =Span({w1}) in C^3

    a vector x =(a,b,c) in W_perp satisfies <w1,x> = 0 => ai + c = 0 => c=-ai
    Thus a vector x in W_perp is x = (a,b,-ai)

    So an orthonormal basis in W would be simply w1/norm(w1) ...but the norm(w1)=0 (i^2 + 1 = 0)

    What am I missing here? Does a basis for W satisfy that it has zero length? Thus it is just the origin. Then would all of C^3 be W_perp?
  2. jcsd
  3. Mar 30, 2010 #2


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    The complex inner product norm <x,y> is defined by (x*)^T y. You are forgetting the complex conjugate.
  4. Mar 30, 2010 #3
    Ahh...I forgot to remember that a norm for F=C requires we take the complex conjugate of the 2nd vector.

    You beat me to to it. :-)
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