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 **R**^{n} are multivariate normal distributions with expected value **0** and variance σ^{2}*I*_{n}, (where *I*_{n} = the *n*×*n* identity matrix), for some positive number σ^{2}.