Solve Eigenvalue Problem A: Proving (λI-A)=0 with Simetric Matrices

[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 B^2v \bullet v=0 (dot product is also v)

so v is orthogonal to B^2v



what to do now?

 

[ardie]

have u tried reading your own post?

 

[nhrock3]

have u tried reading your own post?

in latex not working here don't know why

yes i have tried to read this

even without the its very simple latex

 

[ardie]

ok i can read it now, so you are given that

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

what is v?
so you are given this:

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

and you need to prove this?

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