In mathematics, a nilpotent matrix is a square matrix that is nilpotent. For example, a matrix of the following form:

This is an example of a 4×4 nilpotent matrix. Notice the non-zero superdiagonal. The Characteristic feature of this matrix is:

The super-diagonal keeps 'shifting' diagonally up, until one gets the null matrix.

There is a classification theorem showing that this is typical: a nilpotent matrix is similar to a block matrix, with diagonal square blocks generalising this type, and other blocks zero.