  We consider the problem of estimating a rank-one nonsymmetric matrix under
additive white Gaussian noise. The matrix to estimate can be written as the
outer product of two vectors and we look at the special case in which both
vectors are uniformly distributed on spheres. We prove a replica-symmetric
formula for the average mutual information between these vectors and the
observations in the high-dimensional regime. This goes beyond previous results
which considered vectors with independent and identically distributed elements.
The method used can be extended to rank-one tensor problems.
