I'm trying to implement in Mathematica a method for analytical solution of reaction kinetics.
Numerically it is not a problem but in a symbolic form, one have to rearrange by hand columns of EigenVectors in order to get the "right" result.
Please check www.biokin.com/tools/pdf/Koro11-Kinetics-Maple-Chap2.pdf, page 41-44 for example.
I'm using a matrix
K={{-k1 - k2, 0, 0, 0}, {k1, 0, 0, 0}, {k2, 0, -k3, k4}, {0, 0, k3, -k4}}
as pointed out in example on page 43. {vals,vect}=Eigensystem[K] gives a different answer.
As a result my final solution vect.DiagonalMatix[Exp[vals]].Inverse[vect] is a mess.
Is there way to Sort the answer when it is in symbolic form? Or how to "force" Mathematica, not to arrange Eigenvalues and Eigenvectors?
The sorting of Eigenvalues and Eigenvectors is entirely arbitrary, the important part is that that you get the right ones together.
The issue with your code is that vect is a list of the eigenvectors, which when you use it as a matrix is a matrix whose rows are the eigenvectors, whereas you need a matrix whose columns are the eigenvectors. Use Transpose to fix this. Once you've done this, if you simultaneously permute the eigenvectors and eigenvalues nothing changes:
randsamp = RandomSample[Range[4]];
vals[[randsamp]]
Transpose@vect[[randsamp]].DiagonalMatrix[Exp[vals[[randsamp]] t]].Inverse[
Transpose@vect[[randsamp]]] // Simplify
Also there is a specific stack exchange site for Mathematica: http://mathematica.stackexchange.com