Abstract
Comon showed using the Darmois-Skitovitch theorem that under mild assumptions a real-valued random vector and its linear image are both independent if and only if the linear mapping is the product of a permutation and a scaling matrix. In this work, a much simpler, direct proof is given for this theorem and generalized to the case of random vectors with complex values. The idea is based on the ...
Abstract
Comon showed using the Darmois-Skitovitch theorem that under mild assumptions a real-valued random vector and its linear image are both independent if and only if the linear mapping is the product of a permutation and a scaling matrix. In this work, a much simpler, direct proof is given for this theorem and generalized to the case of random vectors with complex values. The idea is based on the fact that a random vector is independent if and only if locally the Hessian of its logarithmic density is diagonal.