The term "Adjoint" appears in many different mathematical areas and for sometimes seemingly different kinds of things. Wikipedia says -- "In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism: if $A$ is adjoint to $B$, then there is typically some formula of the type" $$ \left( A x, y \right) = \left(x, B y\right) $$ Also, Wikipedia goes on to give examples and a few of them I repeat here:
- Hermitian Adjoint of a Linear Operator
- Adjoint Equation (as used in Differential Operators)
- Adjoint Matrix
And, there are other examples.
My question is about how and where was this term chosen. Better yet, who was first to start using it. Every time I see this word in a text or paper I am always thinking "There has to be a better more descriptive term to use".