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Homework Help: Eigenspace of A?

  1. May 21, 2006 #1
    So the question states:
    Let A be a 6x6 matrix with characteristic equation (x^2)(x-1)(x-2)^3=0
    What are the possible dimensions of eigenspaces of A?
    so..
    eigen values possible are
    x=1,x=0,x=2
    for x = 0
    dimension 0?
    for x = 1
    I would say at dimension 0 or 1

    x = 2
    Dimension 0, 1, 2, 3
    They have for x= 0
    1 or 2
    for x = 1
    1 dimension
    for x =2: 1,2,or 3
    I am not sure how they got these answers. Any help would be appreciated.
     
  2. jcsd
  3. May 21, 2006 #2

    JFo

    User Avatar

    for a given eigenvalue [itex]\lambda[/itex], the dimension of the corresponding eigenspace [itex]E_{\lambda}[/itex] must satisfy

    [tex] 1 \leq dim(E_{\lambda}) \leq multiplicity(\lambda) [/tex]
     
    Last edited: May 21, 2006
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