  We propose to analyse the statistical properties of a sequence of vectors
using the spectrum of the associated Gram matrix. Such sequences arise e.g. by
the repeated action of a deterministic kicked quantum dynamics on an initial
condition or by a random process. We argue that, when the number of time-steps,
suitably scaled with respect to $\hbar$, increases, the limiting eigenvalue
distribution of the Gram matrix reflects the possible quantum chaoticity of the
original system as it tends to its classical limit. This idea is subsequently
applied to study the long-time properties of sequences of random vectors at the
time scale of the dimension of the Hilbert space of available states.
