Solving simultaneous equations

[bld12345]

I have the following matrix solution problem.

A-1 * C * D-1 * A * v = v

where C is a square matrix (integer values). A & D are diagonal matrices. (A-1 and D-1 are inverse matrices) The diagonal elements of D are the column sums of the matrix C. The diagonal elements of A also are integer valued). v is a vector of variables whose values I want to solve for.

I cannot figure out how I can get Maple to do this. Do I need to use some other software? It seems to me that I should be able to obtain a soltion to the problem. Is there a reason why there may be no solution?

Thanks.

 

[IRstuff]

There are lots of reasons why there may be no solution, starting with the possibility that you have a singular matrix.

If you are using Maple, you are not in the right forum, since this is a Matlab forum.

TTFN

 

[electricpete]

The standard eigenvalue problem has a format something like:
Q*v = lambda*v
where Q is N*N, v is N*1 and lambda is a scalar 1*1.

Let's define a matrix Q = A-1 * C * D-1 * A

Your equation is then:
Q*v = v

That's an eigenvalue problem where you have assumed lambda=1. But if 1 is not the eigenvalue associated with matrix Q, there will be no solution.

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[electricpete]

Check if det(Q-I)=0. If not there will be no solution.

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