On the explicit formula for Gauss-Jordan elimination
Nam Van Tran, Julia Justino, Imme van den Berg
TL;DR
This paper provides a direct inductive proof that the elements in the intermediate matrices of Gauss-Jordan elimination are quotients of minors, clarifying the explicit formula for this process.
Contribution
It offers a new, straightforward proof of the explicit formula for Gauss-Jordan elimination elements, avoiding previous determinant identities.
Findings
Elements are quotients of minors during elimination
Provides a direct inductive proof of the explicit formula
Clarifies the structure of intermediate matrices
Abstract
The elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure have the form of quotients of minors. Instead of the proof using identities of determinants of \cite{Li}, a direct proof by induction is given.
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