33 lines
1.1 KiB
Markdown
33 lines
1.1 KiB
Markdown
---
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title: "Adjoint"
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chunk: 1/1
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source: "https://en.wikipedia.org/wiki/Adjoint"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T07:22:59.225743+00:00"
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instance: "kb-cron"
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---
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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
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(Ax, y) = (x, By).
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Specifically, adjoint or adjunction may mean:
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Adjoint of a linear map, also called its transpose in case of matrices
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Hermitian adjoint (adjoint of a linear operator) in functional analysis
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Adjoint endomorphism of a Lie algebra
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Adjoint representation of a Lie group
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Adjoint functors in category theory
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Adjunction (field theory)
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Adjunction formula (algebraic geometry)
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Adjunction space in topology
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Conjugate transpose of a matrix in linear algebra
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Adjugate matrix, related to its inverse
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Adjoint equation
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The upper and lower adjoints of a Galois connection in order theory
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The adjoint of a differential operator with general polynomial coefficients
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Kleisli adjunction
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Monoidal adjunction
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Quillen adjunction
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Axiom of adjunction in set theory
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Adjunction (rule of inference) |