# Eigenvector and eigenvalues

1. Oct 29, 2006

### greisen

Hey all,

I have two matrices A,B which commute than I have to show that these eigenvectors provide a unique classification of the eigenvectors of H?

From these pairs of eigenvalue is it possible to obtain the eigenvectors?

I dont quite know how to procede any suggestions?

2. Oct 29, 2006

### StatusX

What is H?

3. Oct 29, 2006

### HallsofIvy

Staff Emeritus
This makes no sense. Obviously, the eigenvectors of A and B will tell you nothing about the eigenvectors of some arbitrary third matrix H. What relationships are there between A, B, and H?

Yes. Look closely at how A and B are related to H.

4. Oct 29, 2006

### greisen

Sorry not H but A the same matrix

5. Oct 29, 2006

### StatusX

So you're asking if the eigenvectors of B determine the eigenvectors of A, given that A and B commute? This doesn't sound right, since the identity matrix commutes with everything. You can narrow down the possible eigenvectors of A, but you won't get a "unique classification."

6. Oct 30, 2006

### greisen

to see if I understand correctly - let's assume that the matrix A har the eigenvalues {1,2,2} and the matrix B has the eigenvalues {-1,1,1} - then it is possible to construct the eigenvectors of B according to the common unique pairs of A and B( (1,1),(2,1),(2,-1)) giving the following eigenvectors: (1,0,0) , (0,1,1) , (0,-1,1) ?

And had it not been possible with unique pairs of eigenvalues would the eigenvectors not be orthogonanle?