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Nilpotent matrices
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Definition of nilpotent matrix
Every nilpotent matrix is similar to one with 1 on subdiagonal blocks and all other entries 0.
A matrix is nilpotent if and only if its only eigenvalue is 0.
Definition of index of nilpotency
Every square matrix is similar the sum of a diagonal and a nilpotent matrix.
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Nilpotent matrices
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Every square matrix is similar the sum of a diagonal and a nilpotent matrix.
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