THEORETICAL DEVELOPMENT AND APPLICATIONS OF RHOTRICES. In this dissertation, the algebra and analysis of rhotrix, a new paradigm of matrix theory, whose goal is central on representation of arrays of numbers in Mathematical rhomboid form, are reviewed. The generalization and axiomatization of the space of real rhotrices are presented. The development of the rhotrix exponent rule and their applications to the study of some special series and polynomial equations over rhotrices are also studied. The classifications of rhotrices into some abstract structures and topological spaces are proposed....