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Re: for higher dimensions?

In article <eb9p00$srh$1 at>,
 "Adriano Pascoletti" <pascolet at> wrote:

> Yes. Use Eigensystem.
> For instance
> M = {{2, 0, -3}, {3, 5, 6}, {1, 1, -1}};esys = Eigensystem[M];

Thanks -- but this, in my interpretation at least, is a 3 X 3 but still 
*two-dimensional* (rows and columns) matrix. 

My current task is to find eigensolutions to a problem that might be 
written most conveniently, with it's indices shown explicitly, as

   M_{i,j,m,n} A_{m,n}  = lambda A_{i,j}  

with M known and the objective being find a set of eigenvalues lambda[k] 
and "eigenmatrices"  A_{i,j}[k] that satisfy this equation.

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