On modular inverse matrices a computation approach

Abstract

This paper describes the proposal of a numerical method and its extension, to compute Modular Inverse Matrices and so, Modular Linear Equations Systems (with one, infinite or no-solution set), with no theoretical limit, inZ_n; considering polynomial and logarithmic time computational complexity. The geometric interpretation of this, implies that elements, such as planes of these vector spaces, interact in the n-dimensional grid. The interaction and ‘movement’ inside the Grid, can only be possible in a discrete way; from one point to another, like digital states. On the other hand, this work also considers applied mathematics in fields such as cryptography. Based on research, it was observed that this method is an algorithm, because it is precise, defined and finite, so it can be programmed in any computer language. This work constitutes a new approach in numerical analysis for modular inverse matrix computation, plotted in 3-axis linearly. Uses and applications of this proposal are diverse.