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Why is the geometric multiplicity more or equal to 1?

  1. Aug 14, 2012 #1
    Hi. I've got a theoretical doubt: why is the geometric multiplicity more or equal to 1?

    Couldn't happen that the eigenspace is the null vector?

    Thanks!
     
  2. jcsd
  3. Aug 14, 2012 #2
    Oh no, it couldn't happen because when I get the eigenvalues I am getting those values for the corresponding vectors different to the null.
     
  4. Aug 14, 2012 #3

    Mark44

    Staff: Mentor

    An eigenvector is defined to be a nonzero vector x such that (A - λI)x = 0. The eigenspace is the space spanned by all of the eigenvectors. Since no eigenvector can be the zero vector, the eigenspace can't be just the space with 0 in it.
     
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