(a):
Additivität:
<v,(f+g)adj(w)>=<(f+g)(v),w>=<f(v)+g(v),w>=
=<f(v),w>+<g(v),w>=<v,fadj(w)>+<v,gadj(w)>=
=<v,fadj(w)+gadj(w)>=<v,(fadj+gadj)(w)>
für alle v,w∈V, also (f+g)adj=fadj+gadj.
Semihomogenität:
<v,(λf)adj(w)>=<(λf)(v),w>=<λ⋅f(v),w>=λ<f(v),w>=
=λ<v,fadj(w)>=<v,λfadj(w)>, also
(λf)adj=λfadj.