1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Depth of an eigen value (generalized eigenspaces)

  1. Oct 13, 2009 #1
    Let [tex]A[/tex] be a matrix and [tex]\mu[/tex] be an eigenvalue of that matrix. Suppose that for some [tex]k[/tex], [tex]\tex{ker}\left(A-\mu I\right)^k=\tex{ker}\left(A-\mu I\right)^{k+1}[/tex]. Then show that [tex]\tex{ker}\left(A-\mu I\right)^{k+r}=\tex{ker}\left(A-\mu I\right)^{k+r+1}[/tex] for all [tex]r\geq0[/tex].
  2. jcsd
  3. Oct 13, 2009 #2


    Staff: Mentor

    What have you tried? Do you know what the kernel of a matrix is?
  4. Oct 13, 2009 #3


    User Avatar
    Science Advisor

    Important point: for any matrix A, A0= 0!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook