# Adjoint equation

From AMS Glossary

## adjoint equation

An equation of the form

**x**_{0}= 𝗟^{T}**x**_{1}, in which the linear operator 𝗟^{T}is the adjoint of the matrix operator 𝗟 that satisfies (𝗟^{T}**x**_{1},**x**_{0}) = (**x**_{1},𝗟**x**_{0}), where**x**_{0}and**x**_{1}are vectors and (,) represents an inner product.If (,) is the standard dot product (Euclidean inner product) then 𝗟

^{T}is simply the transpose of 𝗟.*See*adjoint sensitivity, adjoint model, tangent linear equation.