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Suppose that

1) we do not know the theory of lambda-matrix;

2) we can not see the transition matrix directly (use elementary tranformations).

How can we deduce that the following two matrices are similar? (What we only know is that they have the same eigenvalues, eigenvectors, rank, determinant)

$$ \begin{pmatrix} 1&1&0\\ 0&0&1\\ 0&0&0 \end{pmatrix},\quad \begin{pmatrix} 1&1&1\\ 0&0&1\\ 0&0&0 \end{pmatrix} $$

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    It is not clear what you mean by the theory of lambda-matrix (such a theory does not exist to my knowledge). You might be talking about Jordan normal forms (just a wild guess, no real connection with anything called lambda other than eigenvalues, which apparently you do know about).2013-12-07

2 Answers 2