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nilpotent

C2
Rare

Pronunciation

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    US

      Meanings

      Adjective

      1. having some power or repeated application equal to zero

      Beyond the definition

      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.

        • Domainnilpotent group

          a special kind of group in abstract algebra

      See also

      Similar

      • nil
      • eventually zero

      Shades of meaning

      • square-zero
      • quasinilpotent

      Contrast

      Used with (collocations)

      • nilpotent matrix
      • nilpotent element
      • nilpotent operator
      • nilpotency index

      Word family

      • nilpotency

      Explore

      • zero divisor
      • nilradical

      Forms and spellings

      1 form open this card.

      Main spelling

      • nilpotentadjective