the.com/nilpotent
an element so committed to zero it gets there by repeatedly multiplying itself.
means a number, matrix, or element that becomes zero when raised to some power greater than one, even though it isn't zero itself.
from from latin nil (nothing) plus potent (power) — literally powerful enough to become nothing; coined in 19th-century algebra as mathematicians classified elements by how they behaved under repeated multiplication.
matrix examplestrictly upper triangular matrices are always nilpotent.
not zero divisornilpotents are automatically zero divisors in rings.
opposite ideaidempotent elements stay fixed instead of vanishing.
physics usegrassmann numbers in supersymmetry are nilpotent by design.