1. ## Inner product

Hello,

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

2. $\displaystyle \displaystyle <u+v,w>=<u,w>+<v,w>=-1+(-1)=-2$

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?

3. I found this in the book, but i'm sure how to apply it:

<u,v> = (Av)^T Au

4. $\displaystyle \displaystyle <u,w>=\left(\begin{bmatrix} 2 & 1\\ 1 & 1 \end{bmatrix}\begin{bmatrix} 2\\ 1 \end{bmatrix}\right)^T=\left(\begin{bmatrix} 2 & 1\end{bmatrix}\begin{bmatrix} 2 & 1\\ 1 & 1 \end{bmatrix}\right)=\begin{bmatrix} 5 & 3\end{bmatrix}$

$\displaystyle \displaystyle \begin{bmatrix} 5 & 3\end{bmatrix}*Aw$

Do the same for the other one and add.

5. Thanks! I was also wondering....how do you evaluate this?

|| v - w ||^2

i just wanna see how its written out.

6. <v-w,v-w>=||v||^2-2||v||||w||+||w||^2

7. thanks!