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Math Help - Invariant Subspace Question

  1. #1
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    Invariant Subspace Question

    Show that the plane x^2 + x^3 = 0 is an invariant subspace for the matrix
    A = 1 2 3
    1 2 1
    1 1 2
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  2. #2
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    Quote Originally Posted by flaming View Post
    Show that the plane x^2 + x^3 = 0 is an invariant subspace for the matrix
    A = 1 2 3
    1 2 1
    1 1 2
    What do you mean by x^2, x^3 ?
    If You acquire the notation:
    (x^1, x^2, x^3)
    for a generic element of Your space than the condition
    x^2 + x^3 = 0
    means that the generic element of given subspace is of the form
    x^1(1,0,0)+x^2(0,1,-1)
    Observe that A*(1,0,0) = (1,1,1) which is not an element of our subspace...
    So, explain the notation or give us some clue
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  3. #3
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    i meant x squared and x cubed, as in x raised to the power 2 + x raised to the power 3, hope that helps a little
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  4. #4
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    Quote Originally Posted by flaming View Post
    i meant x squared and x cubed, as in x raised to the power 2 + x raised to the power 3, hope that helps a little
    Well, I don't see how does this equation gives a plane... It gives us two parallel planes x=0, x=-1 neither of which is invariant subspace of A. Probably I still don't understand something.

    I've computed invariant subspaces of A - maybe this will help.
    (1) spanned by a vector (1,-3,2)
    (2) '' (-1-Sqrt[6], 1,1)
    (3) '' (-1+Sqrt[6], 1,1)

    Good luck
    magda
    Last edited by katastrofa_nadfioletu; October 26th 2008 at 04:52 PM.
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