Since a multiplication by an orthogonal matrix is a rotation, the theorem says that if the probability distribution of a random vector is unchanged by rotations, then the components are independent, identically distributed, and normally distributed. In other words, the only rotationally invariant probability distributions on Rn are multivariate normal distributions with expected value 0 and variance σ2In, (where In = the n×n identity matrix), for some positive number σ2.