nilpotent
/nɪlˈpəʊtənt/
nilpotent adjective: such that, for some positive integer n, xⁿ = 0.
Adjective
nilpotent (not comparable)
- 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).
- The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E₈,E₇, E₆, F₄ or G₂ over an algebraically closed field K of characteristic p. This chapter contains...2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129
- Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- Such that the lower central series terminates.
- Admitting a central series of finite length.
- Such that there exists a natural number k with Iᵏ = 0.
- Containing only nilpotent elements.
- Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
Noun
nilpotent (plural nilpotents)
- A nilpotent element.
- The so-called spinor algebra of C(2), the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra of space, including its beautiful representation on the Riemann sphere, and a new proof of the Heisenberg uncertainty principle.2015, Garret Sobczyk, “Part I: Vector Analysis of Spinors”, in arXiv
nilpotent meaning in Tamil
nilpotent in Tamil
- படி சுழி
Forms of nilpotent
| plural | nilpotents |
|---|
Origin of nilpotent
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.
Words formed from nilpotent
- nilpotent algebra
- nilpotent ideal
- nilpotently
- nilpotent orbit
- nilpotent semigroup
- quasinilpotent
Questions about nilpotent
- What does nilpotent mean?
- Nilpotent means such that, for some positive integer n, xⁿ = 0.
- What is nilpotent in Tamil?
- Nilpotent in Tamil is படி சுழி. See Nilpotent meaning in Tamil.
- What part of speech is nilpotent?
- Nilpotent can be an adjective or a noun.
- How do you pronounce nilpotent?
- Nilpotent is pronounced /nɪlˈpəʊtənt/.
Words near nilpotent in the dictionary
Source and license
Adapted from Wiktionary: nilpotent (page history and authors); nilpotent (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Pronunciation audio from Wikimedia Commons, each file under its own free license: LL-Q1860 (eng)-Flame, not lame-nilpotent.wav.
Cite this entry: “nilpotent.” Word.ws, https://word.ws/nilpotent. Based on Wiktionary, CC BY-SA 4.0.