Thank you very much for your answer and your help.

@vv 

Hi,

Thank you very much for your answer, I will try the ReducedRowEchelonForm solution as I definitely have more than one parameters. I guess that this is really asking the machine to do the same thing as a math student would do.

I apologize for my limited knowledge, but I am a little bit curious to understand how would the SmithForm be used to get the eigenvectors in case of one parameter - would it be sufficient to impose that each term in the diagonal matrix returned by SmithForm be an eigenvalue?

Thanks again,

Laureline

@vv 

Hi,

Thank you for your help.

The result of muPAD, using the Moore-Penrose pseudoinverse, looks like (long and complex) ratios of polynomials in the parameters for each coordinate of X. This is the type of results that I am searching  for.

To expose a little bit more of the problem (and to rebound on vv891's answer), this is actually an eigenvector problem, but for which I would know the eigenvalues in advance - the matrix A is (B - e* I), where B is a real matrix with parameters (Bij = Px Py + r where r is a real number), e is an eigenvalue, and I is the identity matrix.

In my 2*2 examples, e=5*I.

Note that, except from the eigenvalues, all other constants/parameters are real.

The eigenvector function is also too slow, as is expected as it has to determine the eigenvalues. I have also tried to use Ker(A)... Without success (the result is not explicit...).

Thank you very much for your help.

Laureline

@Axel Vogt 

And, here is a very concrete example of A:

A=

     | P1 P3 -80 -5I    P1 P4 +12   |

     |P2 P3 + 43       P2 P4 -2 -5I  |

@logiaco 

Hi,

Thank you very much for your interest!

The entries of A are very simple polynomial functions of the parameters; more specifically, each entry Aij of A is of the form:

Aij = Px Py +c

where c is a complex number, and Px and Py are 2 of the 2*N parameters in P. Those parameters are real, non-zero numbers (which I did explicitly mention to Maple using assume, before trying to solve).

Laureline

@Carl Love