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I need to prove whether or not every diagonalisable matrix has pairwise distinct eigenvalues.

My instinct is to think that the statement is true as for a matrix to be diagonalisable there has to exist a basis consisting of the eigenvectors of the matrix. However, I am unsure what is meant by 'pairwise distinct'.

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    $\begingroup$ Look at identity matrix. It's diagonalisable and has only one eigenvalue. $\endgroup$ – user302982 Jan 12 '16 at 15:25
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    $\begingroup$ The matrix $I$ is diagonalisable... but the eigenvalues aren't distinct. $\endgroup$ – user8469759 Jan 12 '16 at 15:25
  • $\begingroup$ @sigmabe Oh, obviously!! Thank you :) $\endgroup$ – Nique Jan 12 '16 at 15:28
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Repeating the obvious counterexample of sigmabe to get this off of the Unanswered queue: the identity matrix clearly is both diagonalizable and has repeated eigenvalues.

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