Explore: Adjoints

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

two right adjoints G and G′, then G and G′ are naturally isomorphic. The same is true for left adjoints. Conversely, if F is left adjoint to G, and G

{\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle A^{*}} on that space according to the

{\displaystyle \psi ^{\dagger }\gamma ^{\mu }\psi } is not even Hermitian. Dirac adjoints, in contrast, transform according to ψ ¯ ↦ ( λ ψ ) † γ 0 . {\displaystyle

mathematics, an element of a *-algebra is called self-adjoint if it is the same as its adjoint (i.e. a = a ∗ {\displaystyle a=a^{*}} ). Let A {\displaystyle

In mathematics, a self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear

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

classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though

thought of as skew-adjoint (since they are like 1 × 1 {\displaystyle 1\times 1} matrices), whereas real numbers correspond to self-adjoint operators. For

An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts. Gradient values with respect