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Question about inner product

  1. Aug 18, 2011 #1
    In one of my tutorial problems, I was asked to verify if the following function
    is a valid inner product

    <[itex]x,y[/itex]>= [itex]x1x2 + y1y2[/itex]

    Note, x=(x1,x2)[itex]^{T}[/itex] and y=(y1,y2)[itex]^{T}[/itex]

    where T means transpose of the matrix

    The tutor said to us the answer is no because it fails the linearity test

    Does it fail the linearity test because of the x1 and y1 terms in front of the x2 and y2 ?
  2. jcsd
  3. Aug 18, 2011 #2
    Try explicitly calculating
    \langle x+y,z\rangle
    and see if it really does equal
    \langle x,z\rangle +\langle y,z\rangle
    If it doesn't then you know it does not satisfy linearity.
  4. Aug 18, 2011 #3
    Does <x,0*y>=0*<x,y>?
  5. Aug 19, 2011 #4


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    Yes, it does. But that doesn't prove anything.
  6. Aug 20, 2011 #5


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    No it doesn't. <x,0>=x1x2.
  7. Aug 21, 2011 #6


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    Oh, Blast! I was interpreting the given inner product wrong!
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