A linear symbolic-based approach to matrix inversion

For inverting a given matrix An×n with numerical and/or symbolic entries the Gaussian Row Operations (GRO) method has been widely applied. One problem with this approach is that the necessary GRO must be performed on an augmented matrix of order n×2n. We present a new method using the standard GRO with considerable reduction in the number of columns. The augmented matrix in the proposed method is of order n×(n+1), where the elements of the last column are all symbolic. Implementation issues for packaging this representation with existing symbolic computation systems are discussed. Computational experience using randomly generated matrices is reported, showing the superiority of this new approach over the conventional technique, namely in terms of both execution time and memory requirement.