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Math Help - Inner product

  1. #1
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    Inner product

    Hello,

    Can you please help me figure this out?

    Let <u,v> be the inner product on R2 generated by

    [ 2 1 ]
    [ 1 1 ]

    <u+v,w>

    u = (2,1)
    v = (-1,1)
    w = (0,-1)

    ....

    I keep getting -2 is my answer, but the book states that it should be -7
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  2. #2
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    \displaystyle <u+v,w>=<u,w>+<v,w>=-1+(-1)=-2

    I get that too.

    However, your post says inner product and this is the dot product. Do you have an inner product definition for this?
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  3. #3
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    I found this in the book, but i'm sure how to apply it:

    <u,v> = (Av)^T Au
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  4. #4
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    \displaystyle <u,w>=\left(\begin{bmatrix}<br />
2 & 1\\ <br />
1 & 1<br />
\end{bmatrix}\begin{bmatrix}<br />
2\\ <br />
 1<br />
\end{bmatrix}\right)^T=\left(\begin{bmatrix}<br />
2 & 1\end{bmatrix}\begin{bmatrix}<br />
2 & 1\\ <br />
1 & 1<br />
\end{bmatrix}\right)=\begin{bmatrix}<br />
5 & 3\end{bmatrix}

    \displaystyle \begin{bmatrix}<br />
5 & 3\end{bmatrix}*Aw

    Do the same for the other one and add.
    Last edited by dwsmith; November 22nd 2010 at 07:45 PM.
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  5. #5
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    Thanks! I was also wondering....how do you evaluate this?

    || v - w ||^2

    i just wanna see how its written out.
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  6. #6
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    <v-w,v-w>=||v||^2-2||v||||w||+||w||^2
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  7. #7
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    thanks!
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