# Thread: Eigenvalues and Matrices

1. ## Eigenvalues and Matrices

Hi

Just after a bit of pointing in the right direction. I have 3 eigenvalues and I am trying to find the matrix that they correspond to.

How do I do it? It is really stumping me!!

Thanks very much

2. Are you trying to find the eigenvectors? Or are you trying to find the original matrix $A$ from its eigenvalues?

3. The original matrix $A$

4. Well, I'm afraid you're not going to be able to determine the matrix A uniquely. There are, in general, infinitely many matrices that are similar to A that have the same eigenvalues. Do you know the size of A?

5. I believe the matrix size is 3x3

6. In that case, assuming you have three distinct eigenvalues, the best you can do is construct a diagonal matrix similar to A. That is, you can construct a diagonal matrix $D$ such that there exists an invertible matrix $P$ such that $A=PDP^{-1}.$ You construct $D$ by simply having your 3 eigenvalues on the main diagonal, and zeros everywhere else.

If you have more conditions on A, you might be able to say more than this.

7. I will give that a go and see how I get on - Cheers

8. Right-ho.

9. It worked - I got the answer I should have - thanks again!!

10. You're very welcome. Have a good one!