Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 341 / Section A / 4 / a

A real linear operator $\mathcal{L}$ on an inner-product space is a positive-definite operator when it is self-adjoint andfor every nonzero $u$ in its domain. In the variational setting one normally requires the stronger uniform estimate $⟨\mathcal{L}u,u⟩\ge c\Vert u{\Vert }_V^2$ for some $c>0$, which is coercivity.