Kinetics of diffusion-assisted reactions in micelles and related microdisperse systems is usually well described in terms of the pair survival probability, which satisfies the diffusion equation with a separation-dependent reaction rate constant determined by the reaction mechanism. Previously, this equation had to be solved numerically. Ln this paper, we present a computationally superior exact matrix form solution for the pair survival probability expressed in terms of eigenmodes of the underlying restricted diffusion problem in the absence of reaction. Irreversible reaction of neutral particles on a spherical micelle surface is considered as a typical example. Several useful approximations are discussed.