Published in Volume XXXIV, Issue 1, 2024, pages 1-22, doi: 10.47743/SACS.2024.1.1

Authors: M. Dehghani Darmian


In this paper, we study and compute the inverse of matrices with parametric entries. We demonstrate that the Gauss-Jordan method can be extended to compute the inverse of parametric matrices, offering a powerful tool for solving systems of linear equations and analyzing parametric systems. Using this new expansion (so-called Gauss-Jordan systems) and also utilizing linearly dependency systems for linear systems involving parameters [4, 5], we introduce the notion of an inverse matrix system for a parametric matrix. In doing so, we decompose the space of parameters into a finite partition and for each partition, we give the corresponding inverse matrix without applying Gröbner systems. We also present an algorithm for computing an inverse system for a given parametric matrix. All mentioned algorithms have been implemented in Maple, and their efficiency and behavior have been experimented on a set of benchmark matrices.

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  title={Efficient Algorithm for Computing Inverse of Parametric Matrices},
  author={M. Dehghani Darmian},
  journal={Scientific Annals of Computer Science},
  organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
  publisher={Alexandru Ioan Cuza University Press, Ia\c si},