Matlab returns inf for the eigenvalues for an overdetermined linear system with the eig function, but the eigenvalues should not return infinit.

I am currently solving linear systems with the eig() function and the eigenvalues that it returns are infinit. How can I solve this? (The eigenvalues should not be infinit)

My actual matrix is rather large so I use a example here for simplicity. We have the following linear differential system:

dx1/dt= 3x1

0 = x1 - x2

The solutions are of the form x= [c1 c2] e^Lt

To solve this differential equation I have the following matrices.

>> A = [1 0;0 0];

>> B = [3 0;1 -1];

With which I use the eig function to solve this problem for L. The eigenvalues that it should return are 3 and 3. But however, it returns:

>> A = [1 0;0 0];

>> B = [3 0;1 -1];

>> E = eig(B,A)

E =

-Inf
   3

How can I solve this? If anything is unclear, please let me know.

[Ryan G]

A is singular. According to the doc, it is trying to solve the problem

A^-1*B = gamma

So if you try to do this in MATLAB it will give you an inf matrix for A inverse due to the singularity. The documentation states that the algorithm will use the QZ method when A is singular. I'm personally not familiar with it.

[Dennis]

Oke, thank you very much. That explains the infinite values. But does someone know how to solve this? With the qz function itself I come to the same answers.

[Ryan G]

What method are you using to determine there are two equivalent eigenvalues? The QZ function will give the same answer because that is how eig processes the singular matrix.

[Dennis]

Maybe I gave an incorrect description. You do indeed get only one eigenvalue. The value of 3. With algebraic multiplicity of 1. But if you know that x1=x2, then you now that the labda must also be equal to three.