Definition & Betydelse | Engelska ordet IDEMPOTENT

Definition av IDEMPOTENT

1. (matematik, datavetenskap) idempotent

Exempel på hur man kan använda IDEMPOTENT i en mening

• the convex hull function from the power set of an affine space over the reals to itself is idempotent;.
• For general rings, elements idempotent under multiplication are involved in decompositions of modules, and connected to homological properties of the ring.
• He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition.
• In other words, effective Chow motives are pairs of smooth projective varieties X and idempotent correspondences α: X ⊢ X, and morphisms are of a certain type of correspondence:.
• A closure operator on the poset P is a function C : P → P that is monotone, idempotent, and satisfies C(x) ≥ x for all x in P.
• A commutative ring in which every element is equal to its square (every element is idempotent) is called a Boolean ring; an example from computer science is the ring whose elements are binary numbers, with bitwise AND as the multiplication operation and bitwise XOR as the addition operation.
• In a paper published in 1958, Schönberg suggested to add a new idempotent to the Heisenberg algebra, and this suggestion was taken up and expanded upon in the 1980s by Basil Hiley and his co-workers in their work on algebraic formulations of quantum mechanics; this work was performed at Birkbeck College where Bohm had become professor of physics in the meantime.
• These healthiness conditions are typically expressed as monotonic idempotent predicate transformers.
• Kleene algebras: a semiring with idempotent addition and a unary operation, the Kleene star, satisfying additional properties.
• The idempotents of a rectangular semigroup form a sub band that is a rectangular band but a rectangular semigroup may have elements that are not idempotent.
• Locally inverse semigroups: a regular semigroup S is locally inverse if eSe is an inverse semigroup, for each idempotent e.
• Generalizing the previous example, if (A,·,≤) is a lattice-ordered group then (A,+,·) is an additively idempotent semifield with the semifield sum defined to be the supremum of two elements.
• These projections are bounded, self-adjoint, idempotent operators that satisfy the orthogonality condition.
• The first-order invariants for the idempotent lifting of the automaton rule (the modified rule formed by omitting the permutation) necessarily behave like the ones for a rectangular band: they have a basis of invariants that flow either leftwards or rightwards at a constant rate without interaction.
• Hiley demonstrated the equivalence between Moyal's characteristic function for the Wigner quasi-probability distribution F(x,p,t) and von Neumann's idempotent within the proof of the Stone–von Neumann theorem, concluding: "In consequence, F(x,p,t) is not a probability density function but a specific representation of the quantum mechanical density operator", thus the Wigner–Moyal formalism exactly reproduces the results of quantum mechanics.
• In mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring.
• In the matrix view of central groupoids, the idempotent elements form the 1s on the main diagonal of a matrix representing the groupoid.

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