Methods for room acoustic analysis based on a single loudspeaker and a single microphone have been extensively studied, both theoretically and experimentally. Although measurement techniques for acquiring and processing spatial information in a room using arrays of loudspeakers and microphones have been recently proposed, the current literature in room acoustics does not describe the use of multiple-input multiple-output (MIMO) systems in a comprehensive manner. The aim of this paper is, therefore, to present an initial theoretical framework for the spatial analysis of enclosed sound fields using an acoustic MIMO system, based on a spherical loudspeaker array and a spherical microphone array. The fundamental characteristics of the system transfer matrix are shown to be invariant to rotation of the arrays, with its rank dependant on the number of reflections in the room. The paper concludes with a simulation study validating the theoretical models.