> IDEMPOTENT and NILPOTENT were used by Benjamin Peirce (1809-1880) in
> 1870 in American Journal of Mathematics (1881): "When an
> expression...raised to a square or higher power...gives itself as the
> result, it may be called idempotent" (OED2).
> (2) As far as I can tell, the currently universally accepted
> definition of idempotent is that which would be obtained from Pierce's
> by striking the phrase "or higher power".
I notice that Webster's New International Dictionary, first edition (1909),
second edition (1934), and third edition addenda all have Peirce's
definition. But the current Tenth Collegiate Dictionary, by the same
publisher, has the modern definition.
The OED2 shows a 1937 citation with the modern definition: "A matrix E is
called idempotent if E^2 = E. (A. A. Albert, Mod. Higher Algebra (1938),
iii 88.
The 1909 and 1934 Webster dictionaries pronounce idempotent with the only
stress on the second syllable. The Third edition addenda shows multiple
pronunciations. And the current Collegiate dictionary gives only the
pronunciation with the primary stress on the first syllable and a secondary
stress on the penult.
Jeff Miller