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Math Help - [SOLVED] eigenspace

  1. #1
    Junior Member
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    [SOLVED] eigenspace

    [FONT=CMR12][LEFT]What is eigenspace? this may seem like a general question but i cant find it online. I understand how to find the basis and eigenvectors, but im lost as to what the eigenspace is.

    Here is the question that i am stuck on



    Given that the eigenvalues of M =
    2 -5 5
    0 3 -1
    0 -1 3
    are 2, 2 and 4.
    (a) Find the eigenspace corresponding to the eigenvalue 2. What is its dimension?
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  2. #2
    Newbie vincent's Avatar
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    the eigenspace of an eigenvalue is the space generated by the eigenvectors coresponding to that eigenvalue. if an eigenvalue has multiplicity greater than 1, its eigenspace can also have a dimension greater than one. in your case finding the eigenspace of 2 is the same as finding a basis for the nullspace of M-2I
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