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!

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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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. :-)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Orthonormal basis for subsets of C^3
  1. Orthonormal Basis (Replies: 7)

  2. Orthonormal basis (Replies: 7)

  3. Orthonormal Basis (Replies: 2)

  4. Orthonormal basis (Replies: 1)

  5. Orthonormal basis (Replies: 1)

Loading...