Given are $n$ random vectors $x_i\in\mathbb{C}^n$ and a vector $y\in\mathbb{C}^n$ which entries (of both $x_i$ and $y$) are drawn iid from some continuous distribution. Every set of $n$ different of those vectors is almost surely linearly independent. What can be said about the vector $a=[a_1,\ldots,a_n]^\top$ which consists of the unique coefficients of the linear combination
$$y = \sum_{i=1}^n a_i x_i \quad\text{?}$$
Can it be proven that $a$ is iid taken from some continuous distribution? Do you have references to the literature which say something about that?