How Ordinary Elimination Became Gaussian Elimination

TL;DR

This paper traces the historical development of Gaussian elimination, highlighting its origins from Newton's method and its evolution into a matrix-based computational technique used in modern linear algebra.

Contribution

It provides a historical analysis of how the method known as Gaussian elimination developed from earlier solutions for linear equations and became a fundamental computational tool.

Findings

Gaussian elimination originated from Newton's notes and was adapted over centuries.

Gauss's notation and approach significantly influenced the method's modern form.

The evolution reflects a shift from manual calculations to matrix-based algorithms.

Abstract

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre called "ordinary," and that Gauss called "common" - is now named after Gauss: "Gaussian" elimination. Gauss's name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.