Nilpotent Matrix

There are two equivalent definitions for a nilpotent matrix.

1. A square matrix whose eigenvalues are all 0.

2. A square matrix A such that A^n is the zero matrix 0 for some positive integer matrix power n, known as the index (Ayres 1962, p. 11).

See also

Eigenvalue, Idempotent Matrix, Matrix Polynomial, Square Matrix

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Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 11, 1962.

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Nilpotent Matrix

Cite this as:

Weisstein, Eric W. "Nilpotent Matrix." From MathWorld--A Wolfram Web Resource.

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