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.
Read more about this topic: Nilpotent Matrix
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