Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    [tex]
    \langle x+y,z\rangle
    [/tex]
    and see if it really does equal
    [tex]
    \langle x,z\rangle +\langle y,z\rangle
    [/tex]
    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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

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

    Landau

    User Avatar
    Science Advisor

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Oh, Blast! I was interpreting the given inner product wrong!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about inner product
Loading...