nilpotent

1 9.9

A matrix or other object that becomes zero when multiplied by itself enough times

adjective
/ˈnɪlˌpoʊtənt/

Specialized

: nilpotente

In linear algebra, a matrix is called nilpotent if there exists a positive integer n such that raising the matrix to the power of n results in the zero matrix.

Examples

A typical characteristic of nilpotent elements is that their powers eventually lead to zero, which simplifies many computations in algebra.
For example, the square of the nilpotent operator in this function space vanishes, demonstrating its critical properties.
While nilpotent groups have no nonidentity special unitary representations, the situation with solvable groups is quite unclear.

Academic text (2018)

Surface Forms

nilpotent positive

Morphology

nilpotent = potent (semi-transparent) = nil + potent

The elements 'nil' and 'potent' are recognizable, but the precise algebraic meaning ('some power equals zero') requires mathematical knowledge and is not fully inferable by a general learner.

Etymology

The word nilpotent combines nil ('nothing' or 'zero') and potent ('power' or 'having power'), so it means 'having the power to become zero'. That's why in mathematics nilpotent describes something that becomes zero when you raise it to a certain power.