ABSTRACT
This appendix introduces and summarizes the most important properties of
adjoint operators in conjunction with differential calculus in vector spaces,
as used for data assimilation. Recall that a nonempty set V is called a vec-
tor space if any pair of elements f, g ∈ V can be: (i) added together by an operation called addition to give an element f + g in V , such that, for any
f, g , h ∈ V , the following properties hold:
f + g = g + f ;
f + (g + h) = (f + g) + h;
There is a unique element 0 in V such that f + 0 = f for all f ∈ V ; For each f ∈ there is a unique element (−f) in V such that f + (−f) = 0.
