The Concept of Differentiation and Integration of Paraletrix: A Generalization of Rhotrix

Abstract

The concepts of matrix-tertions and matrix-noittrets were first introduced by Atanssov, K. T. and Shannon, A. G. [1] as mathematical enrichment exercises involving objects that lie between two-dimensional vectors and 2×2 matrices. This idea was later extended by Ajibade, A. O. [2] through the introduction of rhotrices, mathematical structures positioned between 2×2 and 3×3 matrices. Various multiplication operations for rhotrices, including heart-oriented and row–column multiplications, have been studied extensively, yielding several important results. Building on these developments, the paraletrix was introduced as a generalization of the rhotrix, defined as a structure in which the number of rows and columns need not be equal. In this paper, we extend the theory of paraletrices by introducing the concepts of differentiation and integration with respect to an independent variable occurring in a function, thereby contributing to the broader mathematical framework of generalized matrix-like objects.