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Hi, I know that if two matrices A and B are similar matrices then they must...

Hi,

I know that if two matrices A and B are similar matrices then they must have the same eigenvalues with the same geometric and algebraic multiplicities. However, I was wondering if that statement was equivalent. In order terms, if two matrices have the same eigenvalues with the same algebraic multiplicities, must they be similar? What about geometric multiplicities?

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