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Idempotent analysis information


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

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Idempotent analysis

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

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Idempotence

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(mathematics) Idempotent of a code Idempotent analysis Idempotent matrix Idempotent relation – a generalization of idempotence to binary relations Idempotent (ring...

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Idempotent matrix

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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...

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Tropical analysis

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

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Mathematical analysis

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Idempotent analysisanalysis in the context of an idempotent semiring, where the lack of an additive inverse is compensated somewhat by the idempotent rule...

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Tropical semiring

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

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Idempotent relation

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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...

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Glossary of areas of mathematics

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algebra; it is the theory of ideals in commutative rings. Idempotent analysis the study of idempotent semirings, such as the tropical semiring. Incidence geometry...

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Semiring

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

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Hilbert space

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the ith direct summand Hi. These projections are bounded, self-adjoint, idempotent operators that satisfy the orthogonality condition E i E j = 0 , i ≠ j...

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Network calculus

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Event Systems, Wiley, 1992. V. N. Kolokol'tsov, Victor P. Maslov: Idempotent Analysis and Its Applications, Springer, 1997. ISBN 0792345096. Deterministic...

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Identity function

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

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Semigroup

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

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Quantale

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

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Projection matrix

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{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...

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Clifford analysis

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These are projection operators, otherwise known as mutually annihilating idempotents, on the space of Cln(C) valued square integrable functions on Rn−1. Note...

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List of mathematical proofs

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algebra (to do) Solvable group Square root of 2 Tetris Algebra of sets idempotent laws for set union and intersection Cauchy's integral formula Cauchy integral...

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Normal matrix

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zero is analogous to 0, and the identity matrix is analogous to 1. An idempotent matrix is an orthogonal projection with each eigenvalue either 0 or 1...

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Galois connection

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B → B, known as the associated kernel operator. Both are monotone and idempotent, and we have a ≤ GF(a) for all a in A and FG(b) ≤ b for all b in B. A...

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Matrix of ones

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semi-definite matrix. The matrix 1 n J {\displaystyle {\tfrac {1}{n}}J} is idempotent. The matrix exponential of J is exp ⁡ ( μ J ) = I + e μ n − 1 n J {\displaystyle...

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Nilpotent

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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...

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