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Linear independence and orthogonaliy

  1. Jan 20, 2009 #1
    Please refresh my memory; if a finite set S is L.I., then does this imply the existence of a set T of the same size (i.e. |T| = |S|) so that the elements T are pairwise orthogonal?
     
  2. jcsd
  3. Jan 20, 2009 #2
    If it's in an inner product space, you can use Gram-Schmidt to find T.
     
  4. Jan 31, 2009 #3
    yes. i believe any method you use (eigenspace, nullspace, etc) to find a set that spans T will be mutually orthogonal. i'd probably guess that the basis spanning T would be orthogonal to the basis spanning A as well.
     
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