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Math Help - eigenvalues

  1. #1
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    eigenvalues

    if A and B are similar matrices then the eigenvalues are same. is the converse is true? why?
    thank u
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    Super Member ILikeSerena's Avatar
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    Re: eigenvalues

    Quote Originally Posted by saravananbs View Post
    if A and B are similar matrices then the eigenvalues are same. is the converse is true? why?
    thank u
    Hi saravananbs1

    Do you have any theorems that you can use?
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  3. #3
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    Re: eigenvalues

    consider the two matrices:

    \begin{bmatrix}1&0\\0&1 \end{bmatrix},\ \begin{bmatrix}1&1\\0&1 \end{bmatrix}

    these both have the single eigenvalue 1, but have different Jordan normal forms (in fact both matrices ARE in Jordan normal form), so they cannot be similar.
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  4. #4
    Super Member girdav's Avatar
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    Re: eigenvalues

    A=\begin{pmatrix}0&0\\ 0&0\end{pmatrix} and B=\begin{pmatrix}0&1\\ 0&0\end{pmatrix} gives a counter-example, since both A and B have 0 as eigenvalue with multiplicity 2 but are not similar since the only matrix which is similar to A is A.
    Last edited by girdav; May 26th 2012 at 01:48 PM.
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