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.
Re: Eigenvalues and eigenvectors problem
Quote:
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
