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Related to orthogonality

  1. Apr 19, 2005 #1
    In one of my hw problems we are asked to prove this:

    |X + Y|^2 + |X - Y|^2 = 2|X|^2 + 2|Y|^2

    It seems quite simple: I just expanded both of them (cancelled 2(X dot Y) terms) and came up with the expression on the right. Is there something I am missing or is it really that simple?

    Thanks !
  2. jcsd
  3. Apr 19, 2005 #2


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    It really is!
  4. Apr 19, 2005 #3


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    linear algebra makes many questions in geometry rather trivial. for this reason high schools should teach the subject, instead of calculus, where they usually do an extremely bad job.
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