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please answer this question If the minimal polynomial of a linear operator has distinct roots,its characteristic polynomial also will have distinct roots.

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closed as off-topic by 900 sit-ups a day, Tomás, Brad, hardmath, Daniel Fischer Jul 19 at 22:52

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It's hard to guess what the Question is. Without some additional information, the latter "statement" about distinct roots is not true. Simple example would be the identity matrix, whose minimal polynomial has only the root 1, but whose characteristic polynomial has this root repeated according to multiplicity to match dimension of the operator. –  hardmath Jul 19 at 22:25

1 Answer 1

false. let the operator be the identity matrix.

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... of dimension at least 2. Sorry, couldn't resist :-) –  Doc Nov 19 '13 at 6:20
    
@Doc, sure................. –  Will Jagy Nov 19 '13 at 6:22

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