  After having closely re-examined the notion of a L\'evy's stable vector, it
is shown that the notion of a stable multivariate distribution is more general
than previously defined. Indeed, a more intrinsic vector definition is obtained
with the help of non isotropic dilations and a related notion of generalized
scale. In this framework, the components of a stable vector may not only have
distinct Levy's stability indices $\alpha$'s, but the latter may depend on its
norm. Indeed, we demonstrate that the Levy's stability index of a vector rather
correspond to a linear application than to a scalar, and we show that the
former should satisfy a simple spectral property.
