An algorithm is presented for online learning of rotations. The proposed algorithm involves matrix exponentiated gradient updates and is motivated by the Von Neumann divergence. The additive updates are skew-symmetric matrices with trace zero which comprise the Lie algebra of the rotation group. The orthogonality and unit determinant of the matrix parameter are preserved using matrix logarithms and exponentials and the algorithm lends itself to interesting interpretations in terms of the computational topology of the compact Lie groups. The stability and the computational complexity of the algorithm are discussed.