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MathGroup Archive 2000

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Re: Eigenvectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21918] Re: [mg21896] Eigenvectors
  • From: Ken Levasseur <Kenneth_Levasseur at uml.edu>
  • Date: Fri, 4 Feb 2000 02:54:46 -0500 (EST)
  • Organization: UMass Lowell Mathematical Sciences
  • References: <200002030354.WAA24469@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Birgit:

It could be that the matrix you have has an eigenvalue c of multipicity
greater than 1 and the corresponding eigenspace (nullspace of matrix - c
IdentityMatrix) has dimension less than this multiplicity.  The simplest
example would be the two by two matrix {{a,1},{0,a}}, which has a double
e'value of a and only a one dimensional eigenspace spanned by {1,0}.  

Ken Levasseur
Math Sciences
UMass Lowell

Birgit Hagedorn wrote:
> 
> Greetings,
> 
> What is the difference between the NullSpace (m-xIdentityMatrix) and the
> Eigenvector. I have a 8x8 matrix and 8 eigenvalues.The NullSpace for all
> Eigenvalues is (), but I get 7 Eigenvectors. Can you help me to
> understand the difference or how the Eigenvectors were calculated with
> Mathematica.
> 
> Thanks,
> Birgit


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