mat1110 oblig2 d) y?

[Fam-student]

Hi, i'm quite uncertain as to how i should define y from v in Exercise d). I've been eyeing this paper for way to long now, any kind soul out there with any hints for me? (i've got no idea how to a post picture of the exercise)

[Aleks855]

If you could upload the image to an image hosting site, you could just link it here, so we can take a look at it.

You can use this site, for example: http://imgur.com/

[kiko]

This one, right?

[Fam-student]

[Fam-student]

This one, right?

Glorious, this one indeed, Thanks Kiko!

[DennisChristensen]

Hi, i'm quite uncertain as to how i should define y from v in Exercise d). I've been eyeing this paper for way to long now, any kind soul out there with any hints for me? (i've got no idea how to a post picture of the exercise)

Using orthogonality, we can rescale the $\mathbb{v}^k$'s by a factor of $\frac{1}{\lVert \mathbb{v}^k\rVert}$ to get an orthonormal basis for $\mathbb{R}^n$. Now we can express $\mathbb{y}$ in terms of the eigenvectors as $$\mathbb{y} = c_0\mathbb{v}^0 + \dots c_{n-1}\mathbb{v}^{n-1},$$ where $c_k = \langle \mathbb{y}, \frac{1}{\lVert\mathbb{v}^k\rVert}\mathbb{v}^k \rangle = \frac{1}{\lVert\mathbb{v}^k\rVert}\langle\mathbb{y},\mathbb{v}^k\rangle$. You can now use the known properties of the $\mathbb{v}^k$'s and how they relate to the matrix $A$ to progress further.