Nilpotent Matrix - Additional Properties

Additional Properties

  • If N is nilpotent, then I + N is invertible, where I is the n × n identity matrix. The inverse is given by
where only finitely many terms of this sum are nonzero.
  • If N is nilpotent, then
where I denotes the n × n identity matrix. Conversely, if A is a matrix and
for all values of t, then A is nilpotent.
  • Every singular matrix can be written as a product of nilpotent matrices.

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