  Given $d \ge 1$, let $(A_i)_{i\ge 1}$ be a sequence of random $d\times d$
real matrices and $Q$ be a random vector in $\mathbb{R}^d$. We consider fixed
points of multivariate smoothing transforms, i.e. random variables $X\in
\mathbb{R}^d$ satisfying $X$ has the same law as $\sum_{i \ge 1} A_i X_i + Q$,
where $(X_i)_{i \ge 1}$ are i.i.d. copies of $X$ and independent of $(Q,
(A_i)_{i \ge 1})$. The existence of fixed points that can attract point masses
can be shown by means of contraction arguments. Let $X$ be such a fixed point.
Assuming that the action of the matrices is expanding as well with positive
probability, it was shown in a number of papers that there is $\beta >0$ with
$\lim_{t \to \infty} t^\beta \mathbb{P}(<u,X > >t ) = K\cdot f(u)$, where $u$
denotes an arbitrary element of the unit sphere and $f$ a positive function and
$K \ge 0$. However in many cases it was not established that $K$ is indeed
positive.
  In this paper, under quite general assumptions, we prove that
$\liminf_{t\to\infty} t^{\beta} \mathbb{P} (<u,X >> t)> 0,$ completing, in
particular, the results of arXiv:1111.1756 and arXiv:1206.1709.
