equipped with a binary operator ⋅ {\displaystyle \cdot } is said to be idempotent under ⋅ {\displaystyle \cdot } if x ⋅ x = x {\displaystyle x\cdot x=x}...

algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A {\displaystyle A} is idempotent if and only...

mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is idempotent under the ring's...

In mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring. The lack of an additive inverse in the...

Karoubi envelope (or Cauchy completion or idempotent completion) of a category C is a classification of the idempotents of C, by means of an auxiliary category...

In mathematics, an idempotent binary relation is a binary relation R on a set X (a subset of Cartesian product X × X) for which the composition of relations...

mathematics, an idempotent measure on a metric group is a probability measure that equals its convolution with itself; in other words, an idempotent measure is...

c-semiring is an idempotent semiring and with addition defined over arbitrary sets. An additively idempotent semiring with idempotent multiplication, x...

methods PUT and DELETE, and safe methods are defined as idempotent. Safe methods are trivially idempotent, since they are intended to have no effect on the...

b_{i}=\sum a_{i}\otimes b_{i}a.} Such an element p is called a separability idempotent, since regarded as an element of the algebra A ⊗ A o p {\displaystyle...

still set to 3 after the second application. A pure function is idempotent if it is idempotent in the mathematical sense. For instance, consider the following...

List Free Finite multiset Commutative Finite set Commutative and idempotent Finite permutations Non-commutative[clarification needed] and idempotent...

{\displaystyle \operatorname {ri} } is not a closure operator: although it is idempotent, it is not increasing and if C 1 {\displaystyle C_{1}} is a cube in R...

belongs to is known as a postback. Per RFC 7231, the POST method is not idempotent, meaning that multiple identical requests might not have the same effect...

rank of the code C {\displaystyle C} is n − d {\displaystyle n-d} . The idempotent of C {\displaystyle C} is a codeword e {\displaystyle e} such that e 2...

the same result as if it were applied once (i.e. P {\displaystyle P} is idempotent). It leaves its image unchanged. This definition of "projection" formalizes...

In mathematics, a band (also called idempotent semigroup) is a semigroup in which every element is idempotent (in other words equal to its own square)...

the identity function is always continuous. The identity function is idempotent. Identity matrix Inclusion map Indicator function Knapp, Anthony W. (2006)...

statements fail for rngs. A rng homomorphism f : R → S maps any idempotent element to an idempotent element. If f : R → S is a rng homomorphism from a ring to...

is a morphism g : Y → X such that g ∘ f = idX. Thus f ∘ g : Y → Y is idempotent; that is, (f ∘ g)2 = f ∘ (g ∘ f) ∘ g = f ∘ g. The left inverse g is also...

{\displaystyle e_{a}} are idempotents of End ⁡ ( R R ) ≃ R {\displaystyle \operatorname {End} ({}_{R}R)\simeq R} . The summation of idempotent endomorphisms corresponds...

Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator...

means, that the merge function must be commutative, associative, and idempotent. The intuition behind commutativity, associativity and idempotence is...

the idempotent law for union. Proof: The following proof illustrates that the dual of the above proof is the proof of the dual of the idempotent law for...

{M} :=\mathbf {I} -\mathbf {P} } . P {\displaystyle \mathbf {P} } is idempotent: P 2 = P {\displaystyle \mathbf {P} ^{2}=\mathbf {P} } , and so is M {\displaystyle...

ax^{2}+by^{2}+c=|z|^{2}+c.} A matrix M is idempotent when M2 = M. Idempotent matrices generalize the idempotent properties of 0 and 1. The completion of...

that x n = 0 {\displaystyle x^{n}=0} . The term, along with its sister idempotent, was introduced by Benjamin Peirce in the context of his work on the classification...

semigroup and its idempotents. Each subgroup contains exactly one idempotent, namely the identity element of the subgroup. For each idempotent e of the semigroup...

projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure). In this case, idempotent means that projecting...

equal to its own square is called an idempotent. In any ring, 0 and 1 are idempotents. There are no other idempotents in fields and more generally in integral...