# Don't understand this diagonalizable matrix problem?

• Mar 1st 2012, 03:20 PM
Reefer
Don't understand this diagonalizable matrix problem?
To be honest it has been a while since I've taken Linear Algebra. I'm in my differential equations class and do not recall on how to do this problem.

Given: The diagonalizable matrix A. Show that the eigenvalues of A^2 are the
squares of the eigenvalues of A but that A and A^2 have the same eigenvectors.
• Mar 2nd 2012, 01:28 AM
FernandoRevilla
Re: Don't understand this diagonalizable matrix problem?
Quote:

Originally Posted by Reefer
Given: The diagonalizable matrix A. Show that the eigenvalues of A^2 are the squares of the eigenvalues of A but that A and A^2 have the same eigenvectors.

Hint If $Ax=\lambda x\;(x\neq 0)$ then, $A^2x=A(Ax)=A(\lambda x)=\lambda (Ax)=\lambda \lambda x=\lambda^2x.$