The question : Is there a way for symbolics solution ? ( for solve, X )
Thanks in advance for the time and help.
Yes! Do you have any reason to think that there exists a solution?
BTW, no guess values if you evaluate symbolically.
That way Mathcad does not know the structure of X (the reason for the "pattern match exception" in Valery's post) and you will have to tell MC in some way that X is a 3x3 matrix.
This is what I meant
First Valery's example
Next is your equation - I don't know if Mathcad would ever finish its calculations - I had to stop it, no time to wait anymore. If it would finish and there is a solutons, it would be presented as 9x1 vector, not as 3x3 matrix.
Your equation can be written as M*X=X*D if we additionally demand that a matrix of all zeros would not be allowed.
We can evaluate those two matrix products symbolically and so you get 9 equations for your 9 variables. You can put in some work and investigate, if there is a nontrivial solution, etc.
As of the special way your M and D is constructed, the task can be reduced in solving 3 systems, each of them in only three variables - the three columns of M*X and X*D, which shoul be equal, are independend from the others. Maybe this can help you to decide, if there exists a solution at all, which I doubt (at least not a unique one).
I guess the whole thing is of academic interest only, isn't it?
So you see that we dont have a unique solution for X
In this case you could multiply each columns independendly from the other columns by any value
Mainly a consequence of the fact, that if the symbolic eval of lsolve will return more than one solution, any linear combination of them will be solution, too. This and other details of lsolve (solving systems that are not sqaure) can be found in more detail in the free e-book "Inside Mathcad:Solving" (in case you don't already have it installed, you can get it here: http://communities.ptc.com/community/mathcad/blog/2010/05/13/inside-mathcad-series-programming-solvi...
All possible X form a 3-parametric manifold
So is for example the following matrix X1 also a valid solution