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 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...

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

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...

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...

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...

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...

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...

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

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...

{\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...

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)...

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...

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...

In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing...

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...

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

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...

locally. The operations are commutative. However, they are not necessarily idempotent. The communications infrastructure must therefore ensure that all operations...

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

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...

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

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...

necessarily a zero divisor. An idempotent e {\displaystyle e} is an element such that e2 = e. One example of an idempotent element is a projection in linear...

In the mathematical discipline of idempotent analysis, tropical analysis is the study of the tropical semiring. The max tropical semiring can be used appropriately...

usual multiplication. An idempotent quantale is a quantale whose multiplication is idempotent. A frame is the same as an idempotent strictly two-sided quantale...