For all orthogonally diagonalizable real matrices, or symmetric real matrices, are all eigenvalues distinct? What would be the proof it is so, or if not, what would be the proof?
Orthogonally diagonalizable or symmetric real matrix - are all eigenvalues distinct?
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linear-algebra
matrices
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1Before asking such a question you might try to think of the most obvious example of _diagonal_ real matrices. In general, while eigenvalues often _happen to be_ distinct, there are very few natural conditions that _force_ them to be distinct. – 2012-12-15
1 Answers
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Nope. For instance, consider the identity matrix. All the eigenvalues are $1$.