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.
>