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. >