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nilpotent

C2
adjective

Pronunciation

UK

  • /nˈɪlpəʊtənt/

US

  • /nˈɪlpoʊtənt/

Description

Imagine something that works for a while but is doomed to fade out completely if you keep applying it. That is the core idea behind "nilpotent." In English, the word is used mainly in mathematics, especially in abstract algebra and linear algebra. It describes an element, matrix, or operator that becomes exactly zero after being multiplied by itself, or applied to itself, enough times. Outside mathematics, people sometimes use it in a figurative way for something that loses all force after repeated use, but that use is much less common.

Examples

  1. 1

    Matrix algebra

    The exercise asks you to decide whether the matrix is nilpotent.

  2. 2

    Ring theory

    In this ring, every nilpotent element lies inside the ideal \(N\).

  3. 3

    Group theory

    The course ends with nilpotent groups and solvable groups.

    • Domain

      nilpotent group

      a special kind of group in abstract algebra

Forms and spellings

1 form open this card.

Main spelling

  • nilpotentadjective