if A and B are similar matrices then the eigenvalues are same. is the converse is true? why? thank u
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Originally Posted by saravananbs 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?
consider the two matrices: 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.
and gives a counter-example, since both and have as eigenvalue with multiplicity but are not similar since the only matrix which is similar to is .
Last edited by girdav; May 26th 2012 at 02:48 PM.
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