  We describe a method for inferring linear causal relations among
multi-dimensional variables. The idea is to use an asymmetry between the
distributions of cause and effect that occurs if both the covariance matrix of
the cause and the structure matrix mapping cause to the effect are
independently chosen. The method works for both stochastic and deterministic
causal relations, provided that the dimensionality is sufficiently high (in
some experiments, 5 was enough). It is applicable to Gaussian as well as
non-Gaussian data.
