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
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.