Adjoint equation

From Glossary of Meteorology

adjoint equation

An equation of the form x0 = 𝗟Tx1, in which the linear operator 𝗟T is the adjoint of the matrix operator 𝗟 that satisfies (𝗟Tx1,x0) = (x1,𝗟x0), where x0 and x1 are vectors and (,) represents an inner product.

If (,) is the standard dot product (Euclidean inner product) then 𝗟T is simply the transpose of 𝗟.
See adjoint sensitivity, adjoint model, tangent linear equation.