the.com/nilpotent
raise it to some power and it just gives up and becomes zero.
means a mathematical object (usually a matrix or ring element) that isn't zero itself, but some power of it is exactly zero.
from from latin nil (nothing) plus potent (having power) — literally 'having the power to become nothing,' coined in 19th-century abstract algebra when mathematicians started classifying elements by how they behave under repeated multiplication.
matrix examplea shift matrix: squares to zero, never zero itself
not zero divisorstronger condition — every nilpotent is a zero divisor
used inlie algebras, differential equations, ring theory
smallest casen where x^n=0 is called the index