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Inner product space vectors

  1. Jul 29, 2014 #1
    1. The problem statement, all variables and given/known data

    Suppose [itex]\vec{u}[/itex], [itex]\vec{v}[/itex] and [itex]\vec{w}[/itex] are vectors in an inner product space such that:

    inner product: [itex]\vec{u},\vec{v}= 2[/itex]
    inner product: [itex]\vec{v},\vec{w}= -6[/itex]
    inner product: [itex]\vec{u},\vec{w}= -3[/itex]

    norm[itex](\vec{u}) = 1[/itex]
    norm[itex](\vec{v}) = 2[/itex]
    norm[itex](\vec{w}) = 7[/itex]


    innerproduct: ([itex]\vec{2v-w},\vec{3u+2w}[/itex])

    2. Relevant equations

    [itex]\vec{u}[/itex], [itex]\vec{v}[/itex] and [itex]\vec{w}[/itex][itex]\in[/itex]Rn .The inner product type is not specified (ie. euclidean, weighted ect...)

    3. The attempt at a solution

    Im not sure where to start. This seems like a very simple problem, but im confused on where to start. I cant expand inner products and solve for v,u or w since the inner product formula is not known. I also cant expand inner product([itex]\vec{2v-w},\vec{3u+2w}[/itex]) since I dont know the inner product formula. All I can think of doing right now is expanding norm[itex](\vec{u},\vec{v},\vec{w})[/itex] to equal [itex]\sqrt{innerproduct(\vec{u},\vec{u}})[/itex], [itex]\sqrt{innerproduct(\vec{v},\vec{v}})[/itex], [itex]\sqrt{innerproduct(\vec{w},\vec{w}})[/itex] but that gets me no where as well.
    Can someone give a point in the right direction?
    Thanks in advance!
    Last edited: Jul 29, 2014
  2. jcsd
  3. Jul 29, 2014 #2


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    You should look up what properties a function has to satisfy to be considered an inner product.
  4. Jul 29, 2014 #3
    ahh yes, the algebraic properties of inner product spaces. Of course!

    edit* its -101
    Last edited: Jul 29, 2014
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