1. Eigenvalues and eigenvectors problem

Let A and B be similar matrices, so B=S-1AS for some non singular matrix S.

(a) Prove that A and B have the same characteristic polynomial.

(b) Explain why similar matrices have the same eigenvalues. Do they have the same eigenvectors?

2. Re: Eigenvalues and eigenvectors problem

Originally Posted by christianwos
Let A and B be similar matrices, so B=S-1AS for some non singular matrix S.

(a) Prove that A and B have the same characteristic polynomial.

(b) Explain why similar matrices have the same eigenvalues. Do they have the same eigenvectors?