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Definition of Idempotent
1. Adjective. Unchanged in value following multiplication by itself. "This matrix is idempotent"
Definition of Idempotent
1. Adjective. (mathematics) (computing) Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed. ¹
2. Adjective. (mathematics) ''Said of an element of an algebraic structure (such as a group or semigroup) with a binary operation'': that when the element operates on itself, the result is equal to itself. ¹
3. Adjective. (mathematics) ''Said of a binary operation'': that all of the distinct elements it can operate on are idempotent (in the sense given just above). ¹
4. Noun. An idempotent ring or other structure ¹
¹ Source: wiktionary.com
Definition of Idempotent
1. [n -S]
Lexicographical Neighbors of Idempotent
Literary usage of Idempotent
Below you will find example usage of this term as found in modern and/or classical literature:
1. Spinors, Clifford, and Cayley Algebras by Robert Hermann (1974)
"Now we shall consider some examples of idempotent decompositions. ... idempotent
DECOMPOSITION FOR THE QUATERNIONS Let H denote the quaternions, ..."
2. Convex Optimization & Euclidean Distance Geometry by Jon Dattorro (2005)
"EI idempotent matrices Projection matrices are square and defined by idempotence,
... The transpose of an idempotent matrix remains idempotent; PTPT=PT. ..."
3. Proceedings of the London Mathematical Society by London Mathematical Society (1908)
"Axn, and a fortiori A, must therefore contain an idempotent element.* The converse
of this theorem is that an algebra, every one of whose elements is ..."
4. Linear Associative Algebra by Benjamin Peirce (1882)
"There must be in this group an idempotent or a nilpotent unit. ... The idempotent
unit of the fourth group can even be made the basis of the whole algebra, ..."
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