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  2. Adjoint functors - Wikipedia

    en.wikipedia.org/wiki/Adjoint_functors

    The definition via hom-sets makes symmetry the most apparent, and is the reason for using the word adjoint. The definition via counit–unit adjunction is convenient for proofs about functors that are known to be adjoint, because they provide formulas that can be directly manipulated. The equivalency of these definitions is quite useful.

  3. Adjugate matrix - Wikipedia

    en.wikipedia.org/wiki/Adjugate_matrix

    In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [ 1 ] [ 2 ] It is occasionally known as adjunct matrix , [ 3 ] [ 4 ] or "adjoint", [ 5 ] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose .

  4. Adjoint - Wikipedia

    en.wikipedia.org/wiki/Adjoint

    Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type (Ax, y) = (x, By). Specifically, adjoint or adjunction may mean: Adjoint of a linear map, also called its transpose in case of matrices; Hermitian adjoint (adjoint of a linear operator) in functional analysis

  5. Hermitian adjoint - Wikipedia

    en.wikipedia.org/wiki/Hermitian_adjoint

    In mathematics, specifically in operator theory, each linear operator on an inner product space defines a Hermitian adjoint (or adjoint) operator on that space according to the rule A x , y = x , A ∗ y , {\displaystyle \langle Ax,y\rangle =\langle x,A^{*}y\rangle ,}

  6. Conjugate transpose - Wikipedia

    en.wikipedia.org/wiki/Conjugate_transpose

    The conjugate transpose "adjoint" matrix should not be confused with the adjugate, ⁡ (), which is also sometimes called adjoint. The conjugate transpose of a matrix A {\displaystyle \mathbf {A} } with real entries reduces to the transpose of A {\displaystyle \mathbf {A} } , as the conjugate of a real number is the number itself.

  7. Tensor-hom adjunction - Wikipedia

    en.wikipedia.org/wiki/Tensor-hom_adjunction

    In mathematics, the tensor-hom adjunction is that the tensor product and hom-functor ⁡ (,) form an adjoint pair: ⁡ (,) ⁡ (, ⁡ (,)). This is made more precise below. The order of terms in the phrase "tensor-hom adjunction" reflects their relationship: tensor is the left adjoint, while hom is the right adjoint.

  8. Help:Displaying a formula - Wikipedia

    en.wikipedia.org/wiki/Help:Displaying_a_formula

    This is not a problem with a block displayed formula, and also typically not with inline formulas that exceed the normal line height marginally (for example formulas with subscripts and superscripts). The use of LaTeX in a piped link or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to ...

  9. Universal quantification - Wikipedia

    en.wikipedia.org/wiki/Universal_quantification

    In category theory and the theory of elementary topoi, the universal quantifier can be understood as the right adjoint of a functor between power sets, the inverse image functor of a function between sets; likewise, the existential quantifier is the left adjoint. [3] For a set , let denote its powerset.