Search for "Adjoint functors" in article titles:

1. Adjoint functors: In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being ... (Relationship between two functors abstracting many common constructions) [100%] 2024-01-11 [Adjoint functors]
2. Formal criteria for adjoint functors: In category theory, a branch of mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor. One criterion is the following, which first appeared in Peter J. [63%] 2023-11-25 [Adjoint functors]

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1. Adjoint functor: A concept expressing the universality and naturalness of many important mathematical constructions, such as a free universal algebra, various completions, and direct and inverse limits. Let $ F : \mathfrak K \rightarrow \mathfrak C $ be a covariant functor in one argument from ... (Mathematics) [93%] 2023-09-23
2. Adjoint (operator theory): In mathematics, the adjoint of an operator is a generalization of the notion of the Hermitian conjugate of a complex matrix to linear operators on complex Hilbert spaces. In this article the adjoint of a linear operator M will be ... (Operator theory) [80%] 2023-06-13
3. Adjoint: In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type Specifically, adjoint or adjunction may mean. [80%] 2022-11-23 [Mathematical terminology]
4. Appoint: APPOINT a-point': This word is used for the expression of a large variety of ideas and the translation of almost as many words. naqabh = "stipulate" (Genesis 30:28). paqadh = "put into office" (Genesis 41:34; Numbers 1:50; Esther ... [57%] 1915-01-01
5. Adjoint action: of a Lie group The linear action on the Lie algebra $\frak g$ of the Lie group $G$, denoted by $\operatorname{Ad} : G \rightarrow \operatorname{GL} (\frak g )$, that is defined as follows: Each element $g$ of $G$ induces an ... (Mathematics) [56%] 2023-10-17
6. Adjoint bundle: In mathematics, an adjoint bundle is a vector bundle naturally associated to any principal bundle. The fibers of the adjoint bundle carry a Lie algebra structure making the adjoint bundle into a (nonassociative) algebra bundle. [56%] 2022-08-14 [Lie algebras] [Vector bundles]...
7. Adjoint operator: A linear operator $A^*\colon Y^* \rightarrow X^*$ (where $X^*$ and $Y^*$ are the strong duals of locally convex spaces $X$ and $Y$, respectively), constructed from a linear operator $A\colon X \rightarrow Y$ in the following way. Let the ... (Mathematics) [56%] 2023-09-07
8. Adjoint representation: In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if ... (Mathematical term) [56%] 2023-09-25 [Representation theory of Lie groups] [Lie groups]...
9. Adjoint group: The adjoint group of a linear group $G$ is the linear group $\def\Ad{\mathop{\textrm{Ad}}} \Ad G$ which is the image of the Lie group or algebraic group $G$ under the adjoint representation (cf. Adjoint representation of a ... (Mathematics) [56%] 2023-10-25
10. Dirac adjoint: In quantum field theory, the Dirac adjoint defines the dual operation of a Dirac spinor. The Dirac adjoint is motivated by the need to form well-behaved, measurable quantities out of Dirac spinors, replacing the usual role of the Hermitian ... (Physics) [56%] 2023-10-09 [Quantum field theory] [Spinors]...
11. Adjoint surface: A surface $Y$ that is in Peterson correspondence with a given surface $X$ and is, moreover, such that the asymptotic net on $Y$ corresponds to a conjugate net $\sigma$ on $X$ with equal invariants, and vice versa. The adjoint surface ... (Mathematics) [56%] 2023-10-12 [Geometry]
12. Adjoint matrix: Hermitian adjoint matrix, of a given (rectangular or square) matrix $A = \left\Vert{a_{ik}}\right\Vert$ over the field $\mathbb{C}$ of complex numbers The matrix $A^*$ whose entries $a^*_{ik}$ are the complex conjugates of the entries ... (Mathematics) [56%] 2023-08-06 [Linear and multilinear algebra] [ matrix theory]...
13. Adjoint equation: An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts. Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation. [56%] 2023-11-09 [Differential calculus]
14. Adjoint space: of a topological vector space $E$ The vector space $E^{*}$ consisting of continuous linear functions on $E$. If $E$ is a locally convex space, then the functionals $f\in E^{*}$ separate the points of $E$ (the Hahn–Banach theorem). (Mathematics) [56%] 2023-09-20
15. Adjoint module: contragradient module, dual module The module of homomorphisms of a given module into the ground ring. More precisely, let $ M $ be a left module over a ring $ R $. (Mathematics) [56%] 2023-08-24
16. Self-adjoint: In mathematics, and more specifically in abstract algebra, an element x of a *-algebra is self-adjoint if \displaystyle{ x^*=x }[/math]. A self-adjoint element is also Hermitian, though the reverse doesn't necessarily hold. (Element of algebra where x* equals x) [56%] 2023-12-16 [Abstract algebra] [Linear algebra]...
17. Adjoint connections: Linear connections $ \Gamma $ and $ \widetilde \Gamma $ such that for the corresponding operators of covariant differentiation $ \nabla $ and $ \widetilde \nabla $ there holds $$ Z B ( X , Y ) = B ( \nabla _ {Z} X , Y ) + B ( X , {\widetilde \nabla } _ {Z} Y ) + 2 \omega ... (Mathematics) [56%] 2023-11-06
18. Adjoint filter: In signal processing, the adjoint filter mask \displaystyle{ h^* }[/math] of a filter mask \displaystyle{ h }[/math] is reversed in time and the elements are complex conjugated. Its name is derived from the fact that the convolution with the adjoint ... [56%] 2024-06-02 [Digital signal processing]