Depth of an eigen value (generalized eigenspaces)

  • #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].
 

Answers and Replies

  • #2
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What have you tried? Do you know what the kernel of a matrix is?
 
  • #3
HallsofIvy
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Important point: for any matrix A, A0= 0!
 

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