Mathematical terminology


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 (Ax, y) = (x, By). Specifically, adjoint or adjunction may mean: * Adjoint of a linear map, also called its transpose * Hermitian adjoint (adjoint of a linear operator) in functional analysis * Adjoint endomorphism of a Lie algebra * Adjoint representation of a Lie group * Adjoint functors in category theory * Adjunction (field theory) * Adjunction formula (algebraic geometry) * Adjunction space in topology * Conjugate transpose of a matrix in linear algebra * Adjugate matrix, related to its inverse * Adjoint equation * The upper and lower adjoints of a Galois connection in order theory * The adjoint of a differential operator with general polynomial coefficients * Kleisli adjunction * Monoidal adjunction * Quillen adjunction * Axiom of adjunction in set theory * Adjunction (rule of inference)This article includes a list of related items that share the same name (or similar names). If an internal link incorrectly led you here, you may wish to change the link to point directly to the intended article. (Wikipedia).

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10 Adjoint state method

We show the connection between the method of adjoints in optimal control to the implicit function theorem ansatz. We relate the costate or adjoint state variable to Lagrange multipliers.

From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)

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Algebraic properties of the adjoint. Null space and range of the adjoint. The matrix of T* is the conjugate transpose of the matrix of T.

From playlist Linear Algebra Done Right

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Adjoint / Daggered Operators in Quantum Mechanics

In this video, we will explain adjoint operators in quantum mechanics. First of all, for any operator A, we can define its adjoint, A-dagger, via this equation. The idea behind this is, that while operators in quantum mechanics usually act towards the right, adjoint operators act to the le

From playlist Quantum Mechanics, Quantum Field Theory

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Matrices | Adjoint of a Matrix (Examples) | Don't Memorise

What is the Adjoint of a Matrix? ✅To learn more about, Matrices, enroll in our full course now: In this video, we will learn: 0:00 how to find adjo

From playlist Matrices

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Matrices | Adjoint of a Matrix | Don't Memorise

What is the Adjoint of a Matrix? To learn more about, Matrices, enroll in our full course now: In this video, we will learn: 0:00 how to find adjoin

From playlist Matrices

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Adverbs of degree are words that describe or modify adjectives or adverbs. They are a special type of adverb, so I don't really like to think of them as adverbs. They are best on their own category. These are also called intensifiers or qualifiers. If you want to support the channel, hit

From playlist English Grammar

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Self-Adjoint Operators

Self-adjoint operators. All eigenvalues of a self-adjoint operator are real. On a complex vector space, if the inner product of Tv and v is real for every vector v, then T is self-adjoint.

From playlist Linear Algebra Done Right

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What is an Injective Function? Definition and Explanation

An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez

From playlist Functions

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Adjugate Matrix

In this video, I define the notion of adjugate matrix and use it to calculate A-1 using determinants. This is again beautiful in theory, but inefficient in examples. Adjugate matrix example: Check out my Determinants Playlist:

From playlist Determinants

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Ch 9: What are Hermitian operators? | Maths of Quantum Mechanics

Hello! This is the ninth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll take a look into what Hermitian operators are, and some of their properties. Then, we'll show how we can use our physical intuition to actually derive that physical observables must be Hermi

From playlist Maths of Quantum Mechanics

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Algebraic Topology - 8.1 - Right Adjoints Preserve Limits (RAPL)

Right adjoints preserve limits. Errata: Arkamouli Debnath points out @ 10:04 I mean to write Sets and not Top on the RHS.

From playlist Category Theory Crash Course

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The Inverse of a 4 by 4 Matrix Given the Determinant and Cofactor Matrix

This video explains how to find the inverse matrix of a 4 by 4 matrix using the adjoint method given the determinant and the cofactor matrix.

From playlist Inverse Matrices

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Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: YouTube Playlist:

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

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Definition of an Injective Function and Sample Proof

We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies My Recording Gear (these are my affil

From playlist Injective, Surjective, and Bijective Functions

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[Lesson 13] QED Prerequisites - The Pauli Spin Matrices...from scratch!

The purpose of this video is to motivate the Pauli Spin matrices from first principles. We will use these matrices a lot during the study of QED and it is critical that every aspect of their design and origin is well understood. This video begins by describing what it means to "rotate a sp

From playlist QED- Prerequisite Topics

Related pages

Differential operator | Adjoint functors | Transpose of a linear map | Adjugate matrix | Galois connection | Quillen adjunction | Monoidal adjunction | Conjugate transpose | Hermitian adjoint | Adjoint equation | Adjunction space | Axiom of adjunction