Homework Help: Eigenvalue Problem

1. Jun 27, 2011

nhrock3

A is a simetric metrices nxn. so $$v\in R^n$$ and $$v\neq 0$$

so $$(\lambda I -A)^2=0$$ for some $$\lambda$$

prove that for the same $$v$$ $$(\lambda I -A)=0$$

how i tried to solve it:

i just collected data from the given.

simetric matrices is diagonizable.

$$B=(\lambda I -A)$$

we were given that $$B^2v=0$$

so [TEX]B^2v \bullet v=0[/TEX] (dot product is also v)

so v is orthogonal to [TEX]B^2v[/TEX]

what to do now?

Last edited: Jun 27, 2011
2. Jun 27, 2011

ardie

3. Jun 27, 2011

nhrock3

in latex not working here dont know why

yes i have tried to read this

even without the [tex] its very simple latex

4. Jun 27, 2011

ardie

ok i can read it now, so you are given that
what is v?
so you are given this:
and you need to prove this?