I'm trying to proof the following:
Let $f$ be a continous sesquilinear form on a Hilbertspace $H$ and let $A: H \to H$ be its dedicated Operator such that $$f(u,v) = \langle u, Av \rangle_H \;\;\; \forall u,v \in H.$$ If $A$ is invertible, then $f$ is coercive, i.e. $\exists C > 0: |f(x,x)| \geq C ||x||^2 \; \forall x \in H$.
My attempt: The invertibility of $A$ gives me that $\exists c > 0: ||Ax|| \geq c ||x|| \; \forall x \in H$.
How do I put this in relation to $|f(x,x)| = |\langle x, Ax \rangle|$ or how do I find a lower bound for this term in the first place?