冪べき零れい

Meanings

noun which may take the genitive case particle 'no'

nilpotent

mathematics

Mathematics term. Describes an element or operator for which some power equals zero. Used attributively with の.

冪べき零れい行ぎょう列れつとは、ある自し然ぜん数すう乗じょうで零れい行ぎょう列れつになる行ぎょう列れつのことです。
A nilpotent matrix is a matrix that becomes the zero matrix when raised to some natural number power.
この環かんの元げんは冪べき零れいである。
This element of the ring is nilpotent.

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Kanji

冪power, exponent
零zero, spill, overflow
巾towel, hanging scroll, width

Related words

零れい因いん子し
零因子 (zero divisor) is a related algebraic concept: an element that can multiply with a nonzero element to give zero, while 冪零 means the element itself becomes zero when raised to a power.

Written forms

冪べき零れい
Standard mathematical kanji spelling. 冪 is a specialized character for 'power' (exponentiation).
巾零べきれい
Variant using 巾 as a simplified substitute for 冪. Seen in some mathematical contexts.
べき零れい
Mixed kana-kanji spelling. べき is the kana for 'power', making the reading explicit.

Etymology

From 冪 (べき, 'power' or 'exponent') + 零 (れい, 'zero'). The term is a direct calque of the English 'nilpotent' (from Latin 'nil' meaning nothing and 'potens' meaning power).