There are two equivalent definitions for a nilpotent matrix.
1. A square matrix whose eigenvalues are all 0.
2. A square matrix such that is the zero matrix for some positive integer matrix power , known as the index (Ayres 1962, p. 11).
There are two equivalent definitions for a nilpotent matrix.
1. A square matrix whose eigenvalues are all 0.
2. A square matrix such that is the zero matrix for some positive integer matrix power , known as the index (Ayres 1962, p. 11).
Weisstein, Eric W. "Nilpotent Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NilpotentMatrix.html