Commutative linear operators and their properties

[McLaren Rulez]

Can someone help me with this? When two linear operators commute, I know how to show that they must have at least one common eigenvector. Beyond this fact, what else can be said about commutative operators and their eigenvectors? Further, can they be diagonalized simultaneously (or actually, can they be diagonalized in the first place?), and if so, how can this be proved?

 

[kthouz]

I wished to know about this but no one is responding to this thread. Please, can one somebody help?

 

[Dick]

I wished to know about this but no one is responding to this thread. Please, can one somebody help?

Well, what have you thought about so far? Take 2x2 matrices. Can you find one that can't be diagonalized?

 

[McLaren Rulez]

kthouz, I asked this question again at https://www.physicsforums.com/showthread.php?t=501340

It was a mistake on my part as I had posted this in homework section instead of linear algebra where it belongs. That's why you are not getting replies. If you have a different question from what I asked in the link, try posting a new thread in the linear algebra section. You will definitely get help