An adjunct; a helper.

The adjoint is the transpose of a matrix or vector (if complex numbers are present, this should be accompanied by a complex conjugate of the elements). The adjoint turns rows into columns and vice-versa. Some operators are effectively matrices (linear operators), but cannot, due to storage limitations, be stored explicitly. The adjoint operator must then be formulated as a separate operator either manually or by automatic adjoint software. In 4d-Var, adjoint operators (matrices) help integrate the adjoint variables (cost function gradient vectors) backwards in time.

See Galois connection.