Show that $x' = Ax$ is an attractor if end only if there is a quadratic form $q$ positive definite such that $Dq(x) . Ax < 0$ for all $x \neq 0$

Question

Show that $x' = Ax$ is an attractor if end only if there is a quadratic form $q$ positive definite such that $$Dq(x) . Ax < 0$$ for all $x \neq 0$

Definition: a linear system $x' = Ax$ called attractor if for all $x \in \mathbb{R^n}$ called $$\lim_{t \rightarrow \infty} e^{tA} = 0$$