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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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