nilpotent
/nɪlˈpəʊtənt/adjective, noun
nilpotent is spelled N-I-L-P-O-T-E-N-T: 9 letters. It appears about once in every 15 million words in written English, the 117,098th most frequent word form (wordfreq, 2021 data). As an adjective, nilpotent means “Such that, for some positive integer n, xⁿ = 0” (English Wiktionary, September 2026).
How many letters and syllables are in nilpotent?
| Letters | 9: N-I-L-P-O-T-E-N-T |
|---|---|
| In writing | about once in every 15 million words; the 117,098th most frequent word form |
| Wrong spellings searched | none measured in search |
Sources: letters and syllables from the English Wiktionary's hyphenation or pronunciation; written frequency: wordfreq 3.1 (a 2021 snapshot of Wikipedia, subtitles, news, books, web text and social media).
How common is nilpotent?
Nilpotent appears about once in every 15 million words in written English, the 117,098th most frequent word form in the list.
Source: written frequency: wordfreq 3.1 (a 2021 snapshot of Wikipedia, subtitles, news, books, web text and social media).
How do you pronounce nilpotent?
- /nɪlˈpəʊtənt/
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract). Recordings: LL-Q1860_(eng)-Flame,_not_lame-nilpotent.wav, Wikimedia Commons (author and licence on each file's page).
Forms of nilpotent
- nilpotents plural
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).
What does nilpotent mean?
The meanings the English Wiktionary records, quoted as written there (source below).
adjective
- 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
Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- 3
Such that the lower central series terminates.
- 4
Admitting a central series of finite length.
- 5
Such that there exists a natural number k with Iᵏ = 0.
- 6
Containing only nilpotent elements.
- 7
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
- 1
A nilpotent element.
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).
Nilpotent in Spanish, French, German and Portuguese
In the sense (algebra):
| Language | Words |
|---|---|
| French | nilpotent |
| Spanish | nilpotente |
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract). Translations are Wiktionary's, by sense; a linked word has its own PlainSpell page.
Where does nilpotent come from?
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.
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).