Adjoint equation information

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

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...

in neural networks. The adjoint state space is chosen to simplify the physical interpretation of equation constraints. Adjoint state techniques allow the...

costate equation is related to the state equation used in optimal control. It is also referred to as auxiliary, adjoint, influence, or multiplier equation. It...

^{\mu }\gamma ^{0},} one can derive the adjoint Dirac equation by taking the Hermitian conjugate of the Dirac equation and multiplying on the right by γ 0...

this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics...

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

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...

names for the conjugate transpose of a matrix are Hermitian conjugate, adjoint matrix or transjugate. The conjugate transpose of a matrix A {\displaystyle...

mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions...

self-adjoint operator is an operator equal to its own (formal) adjoint. If Ω is a domain in Rn, and P a differential operator on Ω, then the adjoint of...

can be efficiently calculated by solving the adjoint equation. Methods based on solution of adjoint equations are used in wing shape optimization, fluid...

corresponding adjoint bundle, d A {\displaystyle d_{A}} is the exterior covariant derivative induced by A {\displaystyle A} on the adjoint bundle, and ⋆...

known as adjunct matrix, or "adjoint", though the latter term today normally refers to a different concept, the adjoint operator which for a matrix is...

identity matrix provide a basis for 2 × 2 {\displaystyle 2\times 2} self-adjoint matrices:: 126  ρ = 1 2 ( I + r x σ x + r y σ y + r z σ z ) , {\displaystyle...

differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. A differential...

when working with Fourier transforms. Because Bessel's equation becomes Hermitian (self-adjoint) if it is divided by x, the solutions must satisfy an orthogonality...

side of this equation is the Laplace operator, and the entire equation Δu = 0 is known as Laplace's equation. Solutions of the Laplace equation, i.e. functions...

in that case the techniques of linear programming are applicable. Adjoint equation Newton's method Steepest descent Conjugate gradient Sequential quadratic...