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1. Decomposition: A decomposition is a representation of a given set as the union of a system of pairwise disjoint sets. In discrete geometry one frequently considers the decomposition of some space into closed domains which cover the entire space and whose ... (Mathematics) [100%] 2023-11-14
2. Decomposition: Decomposition or rot is the process by which dead organic substances are broken down into simpler organic or inorganic matter such as carbon dioxide, water, simple sugars and mineral salts. The process is a part of the nutrient cycle and ... (Process in which organic substances are broken down into simpler organic matter) [100%] 2024-05-12 [Anaerobic digestion] [Articles containing video clips]...
3. Spinodal decomposition: A term introduced in the physical description of unmixing of metallic alloys by J.W. Cahn , cf. (Mathematics) [70%] 2023-10-12
4. Gordon Decomposition: In mathematical physics, the Gordon-decomposition (named after Walter Gordon one of the discoverers of the Klein-Gordon equation) of the Dirac current is a splitting of the charge or particle-number current into a part that arises from the ... (Physics) [70%] 2023-09-20 [Equations of physics]
5. Langlands decomposition: In mathematics, the Langlands decomposition writes a parabolic subgroup P of a semisimple Lie group as a product \displaystyle{ P=MAN }[/math] of a reductive subgroup M, an abelian subgroup A, and a nilpotent subgroup N. A key application is ... [70%] 2024-01-08 [Lie groups] [Algebraic groups]...
6. Schur decomposition: In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily equivalent to an upper triangular matrix whose ... [70%] 2023-11-15 [Matrix theory] [Articles containing proofs]...
7. Wold decomposition: A decomposition introduced by H. Wold in 1938 (see ); see also ,. (Mathematics) [70%] 2023-10-21
8. Primary decomposition: In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not ... (In algebra, expression of an ideal as the intersection of ideals of a specific type) [70%] 2023-09-12 [Commutative algebra] [Theorems in ring theory]...
9. Gordon decomposition: In mathematical physics, the Gordon decomposition (named after Walter Gordon) of the Dirac current is a splitting of the charge or particle-number current into a part that arises from the motion of the center of mass of the particles ... (Physics) [70%] 2023-12-01 [Equations of physics]
10. Chemical decomposition: Chemical decomposition, or chemical breakdown, is the process or effect of simplifying a single chemical entity (normal molecule, reaction intermediate, etc.) into two or more fragments. Chemical decomposition is usually regarded and defined as the exact opposite of chemical synthesis. (Chemistry) [70%] 2023-11-30 [Inorganic chemistry] [Organic chemistry]...
11. Cartan decomposition: In mathematics, the Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. (Generalized matrix decomposition for Lie groups and Lie algebras) [70%] 2023-08-23 [Lie groups] [Lie algebras]...
12. Schmidt decomposition: In linear algebra, the Schmidt decomposition (named after its originator Erhard Schmidt) refers to a particular way of expressing a vector in the tensor product of two inner product spaces. It has numerous applications in quantum information theory, for example ... (Process in linear algebra) [70%] 2023-12-26 [Linear algebra] [Singular value decomposition]...
13. Jordan decomposition (of an endomorphism): The Jordan decomposition of an endomorphism $ g $ of a finite-dimensional vector space is the representation of $ g $ as the sum of a semi-simple and a nilpotent endomorphism that commute with each other: $ g = g _{s} + g _ ... (Mathematics) [70%] 2023-10-19
14. Stanley decomposition: In commutative algebra, a Stanley decomposition is a way of writing a ring in terms of polynomial subrings. They were introduced by Richard Stanley (1982). [70%] 2023-12-09 [Commutative algebra]
15. Hamiltonian decomposition: In graph theory, a branch of mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles. Hamiltonian decompositions have been studied both for undirected graphs and for directed graphs. [70%] 2024-01-12 [Graph theory objects]
16. Jordan decomposition (of a function): A canonical decomposition theorem (due to Jordan) for functions of bounded variation of one real variable. Theorem If $f:[a,b] \to\mathbb R$ is a function of bounded variation then there is a pair of nondecreasing functions $f^+$ and ... (Mathematics) [70%] 2024-01-12 [Analysis]
17. Ear decomposition: In graph theory, an ear of an undirected graph G is a path P where the two endpoints of the path may coincide, but where otherwise no repetition of edges or vertices is allowed, so every internal vertex of P ... (Partition of graph into sequence of paths) [70%] 2023-03-22 [Graph theory objects] [Matroid theory]...
18. Continuous decomposition: of a topological space A covering of by pairwise-disjoint non-empty sets satisfying the following condition: For any and any neighbourhood of in there is a neighbourhood of in contained in that is the union of a certain collection ... (Mathematics) [70%] 2023-10-17
19. Semantic decomposition (natural language processing): A semantic decomposition is an algorithm that breaks down the meanings of phrases or concepts into less complex concepts. The result of a semantic decomposition is a representation of meaning. (Natural language processing) [70%] 2023-02-01 [Natural language processing] [Artificial intelligence]...
20. Witt decomposition: of a vector space A decomposition of the space into a direct sum of three subspaces having certain properties. More exactly, let $ V $ be a vector space over a field $ k $ with characteristic different from 2, provided with a metric ... (Mathematics) [70%] 2023-09-22