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

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- Aug 30th 2010, 10:39 AMIan1779Eigenvalues 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 - Aug 30th 2010, 11:05 AMAckbeet
Are you trying to find the eigenvectors? Or are you trying to find the original matrix $\displaystyle A$ from its eigenvalues?

- Aug 30th 2010, 11:12 AMIan1779
The original matrix $\displaystyle A$

- Aug 30th 2010, 11:15 AMAckbeet
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?

- Aug 30th 2010, 11:29 AMIan1779
I believe the matrix size is 3x3

- Aug 30th 2010, 11:32 AMAckbeet
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 $\displaystyle D$ such that there exists an invertible matrix $\displaystyle P$ such that $\displaystyle A=PDP^{-1}.$ You construct $\displaystyle D$ 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. - Aug 30th 2010, 11:36 AMIan1779
I will give that a go and see how I get on - Cheers

- Aug 30th 2010, 11:52 AMAckbeet
Right-ho.

- Aug 30th 2010, 12:07 PMIan1779
It worked - I got the answer I should have - thanks again!!

- Aug 30th 2010, 12:08 PMAckbeet
You're very welcome. Have a good one!