Unimodular Matrix On Compound Mathematical Structures Applications and Results

Abstract

This paper considers knowledge of unimodular matrixes, some compound structural matrix, and their applications. Studying the properties of unimodular matrixes and extending compound structures related to this set of matrixes we give some results. The inverse of an unimodular matrix and the product of two unimodular matrices is also uni-modular. We are generating a finite system of linear equations via a uni-modular matrix with Latex and Python programs. According to the previous results of the transformation theory of the unimodular matrix, we use basic properties such as unimodular, orthogonality, and symmetry. A comparison between the results is mentioned in this article to obtain general conclusions. We deal with the considered results comparing the obtained solutions with the exact ones. We give in particular the numerical results compared with the analytical results using the natural exponential matrix function of real variables and the unimodular matrix can be solved efficiently. Another problem arises if the entries of the inverse matrix are not integers, so it will take longer if done by hand manually. We are sure that their applications are very important. We propose their applications to construct the algebraic structures. In conclusion, mathematically we analyze the exponential function of an unimodular matrix. We describe the symmetry of space which gives accurate results.