I'm studying Trust-region method and there is proof in the book using the follow inequality:
where $B_k$ is a positive definite matrix, i.e, $g_k^TB_kg_k > 0$.
The book says "Using the Cauchy Schwarz inequality we have this". I've tried use the fact, $\|Ax\| \leq \|A\|\cdot\|x\|$, but I couldn't reach the inequality.
Thanks for help