Consider a strongly convex function $g$, that is, for all $x,y$ in the domain and $t\in[0,1]$ we have $$ g(t x + (1-t)y) \le tg(x)+(1-t)g(y) - \frac{1}{2}mt(1-t)||x-y||_2^2 $$ for some $m>0$. Also, let $A$ be a full rank linear tranformation. Define $f = g\circ A$.
Is $f$ strongly convex?
Yes. Note that there are constants $b, c > 0$ such that $b \|x\|_2 \le \|Ax\|_2 \le c \|x\|_2$ for all $x$. So $f \circ A$ is strongly convex if $f$ is strongly convex (but with a different $m$); if $A$ is onto this is if and only if.