Eigenvalues and eigenvectors problem

Let A and B be similar matrices, so B=S^{-1}AS 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?

Please provide explanation. Thank you.

Re: Eigenvalues and eigenvectors problem

Quote:

Originally Posted by

**christianwos** Let A and B be similar matrices, so B=S^{-1}AS 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?

Please provide explanation. Thank you.

Please show us how far you have got.

-Dan