Is this strongly convex?

Question

$f(x)=\frac{1}{2}x^\intercal W x$, where $W$ is positive definite, not necessarily the identity matrix. $\nabla^2 f(x)=W$. Is $f(x)$ strongly convex with the parameter $m={}?$

Answer 1

Strong convexity of $f$ with parameter $m$ is equivalent to $\nabla^2 f(x) \succeq m I$, so in your case, $f$ is strongly convex with parameter $m$ being the smallest eigenvalue of $W$.