Matrix inversion: a computational algebra approach

Abstract

The most widely used computer‐based approach is to use Gauss—Jordan (GJ) row operations. One problem with this approach is that the necessary row operations must be performed on an augmented matrix of order (nby 2n)which becomes very tedious for hand calculations for both instructors as well as their students. We present a new approach based on the GJ row operations principle with considerable reduction in the number of columns. The augmented matrix in the proposed method is of order (n by n +1). A short summary of the algorithm is as follows: Place the matrix A n x n which is to be inverted, along side a column vector R with ri as its ith row element, 1 ≤ i ≤ n,where ri is an unspecified variable. Then perform the same GJ row operation on A and R in such a way that A changes to an identity matrix. It is shown that the matrix of coefficients of r i becomes A‐1. In addition, implementation of this approach on the MAPLE computer algebra system is presented. To the best of our knowledge, this new method is n...