Thread: 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?

Please provide explanation. Thank you.

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?

Please provide explanation. Thank you.

Please show us how far you have got.

-Dan