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

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...

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

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

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...

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...

required to be idempotent. That is, a preclosure operator obeys only three of the four Kuratowski closure axioms. A preclosure operator on a set X {\displaystyle...

to a graph of a function, say, is also a projection. The terms “idempotent operator” and “forgetful map” are also synonyms for a projection. structure...

zero, then T is said to be nilpotent. If T2 = T, then T is said to be idempotent If T = kI, where k is some scalar, then T is said to be a scaling transformation...

construction of certain K-groups in Operator K-theory As stated above, projections are a special case of idempotents. Analytically, orthogonal projections...

(\mathbf {X} ).\end{aligned}}} The matrix PX is idempotent. More generally, the trace of any idempotent matrix, i.e. one with A2 = A, equals its own rank...

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

+ A {\displaystyle A^{+}A} and A A + {\displaystyle AA^{+}} are idempotent operators, as follows from ( A A + ) 2 = A A + {\displaystyle (AA^{+})^{2}=AA^{+}}...

\theta \cos \phi &\sin \theta \sin \phi &\cos \theta \end{pmatrix}},} the idempotent density matrix 1 2 ( 1 + a → ⋅ σ → ) = ( cos 2 ⁡ ( θ 2 ) e − i ϕ sin ⁡...

) {\displaystyle \forall x(f\ (f\ x)=f\ x)} Such functions are called idempotent (see also Projection (mathematics)). An example of such a function is...

representation and Jordan product operators L(a)b = a ∘ b are continuous operators on M for both the weak and strong topology. An idempotent p in a JBW algebra M is...

logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used...

the following properties for S,T ∈ P(E): S ⊆ d(S); d(S) = d(d(S)) (d is idempotent); if S ⊆ T then d(S) ⊆ d(T); if Ω is the set of finite subsets of S then...

{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...

V^{3}\cup V^{4}\cup \cdots .} This means that the Kleene star operator is an idempotent unary operator: ( V ∗ ) ∗ = V ∗ {\displaystyle (V^{*})^{*}=V^{*}} for...