# Eigenvalues and Matrices

• Aug 30th 2010, 10:39 AM
Ian1779
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
• Aug 30th 2010, 11:05 AM
Ackbeet
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 AM
Ian1779
The original matrix \$\displaystyle A\$
• Aug 30th 2010, 11:15 AM
Ackbeet
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 AM
Ian1779
I believe the matrix size is 3x3
• Aug 30th 2010, 11:32 AM
Ackbeet
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 AM
Ian1779
I will give that a go and see how I get on - Cheers
• Aug 30th 2010, 11:52 AM
Ackbeet
Right-ho.
• Aug 30th 2010, 12:07 PM
Ian1779
It worked - I got the answer I should have - thanks again!!
• Aug 30th 2010, 12:08 PM
Ackbeet
You're very welcome. Have a good one!