Basic ideas and notation

The basic idea of adjoint is that the adjoint of a row vector is a column vector. So the adjoint of the equation y=ax₁+bx₂ is two equations, $\hat x_1 = ay$ and $\hat x_2 = by$.

Since we often combine operators by addition, we often code them in the form $y\leftarrow y+ax_1+bx_2$.A convenient notation comes from the C computer language where such assignments are written as y += a*x1+b*x2. I find the ``+='' notation expecially convenient for describing adjoints.