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nilpotent

adj
/nɪlˈpəʊtənt/

Etymology

From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens. Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.

  1. derived from potens — “powerful, strong, potent”
  2. inherited from potent
  3. compounded as nilpotent — “nil + potent”

Definitions

  1. Such that, for some positive integer n, xⁿ = 0.

    • If a square matrix is upper triangular and has zeros on the diagonal, then it is nilpotent (under the usual matrix multiplication).

  2. In any of several technical senses

    In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.

  3. A nilpotent element.

The neighborhood

Derived

nilpotent algebra, nilpotent ideal, nilpotently, nilpotent orbit, nilpotent semigroup, quasinilpotent

Vish — recursive loop

No curated loop yet for nilpotent. Loops are being traced one word at a time while the ingestion pipeline matures.

sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA