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Math Help - Eigenvalues and eigenvectors problem

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    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.
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    Re: Eigenvalues and eigenvectors problem

    Quote Originally Posted by christianwos View Post
    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
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