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Orthonormal Basis

  1. Jul 18, 2009 #1
    1. The problem statement, all variables and given/known data

    True/False:

    The set of vectors [tex]B={(-1,-1,1,1),(1,0,0,0),(0,1,0,0),(-1,-1,1,-1)}[/tex] is an orthonormal basis for Euclidean 4-space [tex]\mathbb{R}^4[/tex].

    2. Relevant equations
    None


    3. The attempt at a solution

    I said false because [tex]\langle (-1,-1,1,1),(-1,-1,1,1) \rangle =2\ne1[/tex], which shows that at least one vector in this set is not a unit vector.

    However, I'm not sure if I'm supposed to use the usual definition for the inner product. Is this implied by the word "Euclidean"?
     
  2. jcsd
  3. Jul 18, 2009 #2

    Dick

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    That looks right. Some of the vectors aren't orthogonal either. "Euclidean" would imply the usual inner product. But even if they left the word "Euclidean" off, I would still use the usual inner product, just because they didn't tell you to use a different one.
     
  4. Jul 18, 2009 #3
    Perfect. Thanks!
     
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