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MathGroup Archive 2006

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Re: Eigensystem[] for higher dimensions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68492] Re: [mg68472] Eigensystem[] for higher dimensions?
  • From: "Adriano Pascoletti" <pascolet at dimi.uniud.it>
  • Date: Tue, 8 Aug 2006 06:28:24 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Yes. Use Eigensystem.
For instance

M = {{2, 0, -3}, {3, 5, 6}, {1, 1, -1}};esys = Eigensystem[M];

The diagonal matrix of the eigenvalues of M is given by

Lambda = DiagonalMatrix[esys[[1]]];

The matrix whose columns are the eigenvector of M by

A = Transpose[esys[[2]]];

Indeed

In[15]:= M.A-A.Lambda//Expand

gives

Out[15]= {{0,0,0},{0,0,0},{0,0,0}}


Adriano Pascoletti

AES wrote ..
> Can the matrix m in Eigensystem[m] be greater than two dimensional?
> 
> And the eigenvectors v correspondingly greater than one dimensional?
> 
> The problem of interest is finding the eigenvalues lambda and 
> eigenarrays A of the equation
> 
>    M A = lambda A
> 
> with A being a (physically nonseparable) two dimensional array and M a
> specified four dimensional array.  I can of course use appropriate 
> indexing to convert these to one and two dimensional quantities, but the
> index transformations can be a pain; the reverse index transformations
> even more ugly; the Mathematica Book doesn't seem to explicitly answer
> the question -- and it's easier to ask it here, and maybe also get some
> useful pointers, than futz around with experiments.
> 


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