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Geometric Multiplicity of Eigenvalues

  1. May 9, 2013 #1
    Could someone please explain to me (with an example if possible) what is the Geometric Multiplicity of Eigenvalues? I cannot understand it from what I have read on the web till now.
    Thanks in advance.
     
  2. jcsd
  3. May 9, 2013 #2

    micromass

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    Let ##\lambda## be an eigenvalue of the linear transformation ##T:V\rightarrow V##.
    We can look at the set of all eigenvectors (plus 0). So we get

    [tex]E_\lambda = \{v\in V~\vert~Tv = \lambda v\}[/tex]

    This is a subspace of ##V## and thus it has a dimension. The dimension of ##E_\lambda## is called the geometric multiplicity of ##\lambda##.
     
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