A space efficient flexible pivot selection approach to evaluate determinant and inverse of a matrix

TL;DR

This paper introduces space-efficient, flexible algorithms for computing matrix determinants and inverses, allowing arbitrary pivot choices and reducing data storage, suitable for educational purposes and handling ill-conditioned matrices.

Contribution

It proposes novel algorithms that improve efficiency and flexibility in matrix determinant and inverse calculations without permutations or extra data storage.

Findings

Handles ill-conditioned matrices effectively

Reduces data storage by decreasing matrix order during computation

Does not require permutations, simplifying implementation

Abstract

This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The algorithms are more efficient as they save unnecessary data storage by reducing the order of the matrix after each iteration in the computation of determinant and incorporating dictionary notation (Chvatal, 1983) in the computation of inverse matrix. These algorithms are highly class room oriented and unlike the matrix inversion method (Khan, Shah, & Ahmad, 2010) the presented algorithm does not need any kind of permutations or inverse permutations.