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Eigenvalue Problem

  1. Jun 27, 2011 #1
    A is a simetric metrices nxn. so [tex]v\in R^n[/tex] and [tex]v\neq 0[/tex]

    so [tex](\lambda I -A)^2=0[/tex] for some [tex]\lambda[/tex]



    prove that for the same [tex]v[/tex] [tex](\lambda I -A)=0[/tex]



    how i tried to solve it:

    i just collected data from the given.

    simetric matrices is diagonizable.

    [tex]B=(\lambda I -A)[/tex]

    we were given that [tex]B^2v=0[/tex]

    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. jcsd
  3. Jun 27, 2011 #2
    have u tried reading your own post? o_O
     
  4. Jun 27, 2011 #3
    in latex not working here dont know why

    yes i have tried to read this

    even without the [tex] its very simple latex
     
  5. Jun 27, 2011 #4
    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?
     
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