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Difference between an eigenspace and an eigenvector ?

  1. Apr 30, 2012 #1
    So I'm a bit confused between these two and can't quite find any useful resources online. So is an eigenspace a special type of eigenvector cause that's how I understand it now.
     
  2. jcsd
  3. Apr 30, 2012 #2

    Fredrik

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    No, an eigenspace is the subspace spanned by all the eigenvectors with the given eigenvalue. For example, if R is a rotation around the z axis in ℝ3, then (0,0,1), (0,0,2) and (0,0,-1) are examples of eigenvectors with eigenvalue 1, and the eigenspace corresponding to eigenvalue 1 is the z axis.
     
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