Fraction-free Linear Algebra

Abstract

Humans and computers hate fractions and square roots. If a matrix problem contains only integers, then a computer algebra system prefers to compute with integers, rather than fractions. However, many standard topics in linear algebra are treated in such a way that students and computers are forced to use fractions or square roots. Alternative treatments are fraction-free or square root free. In this talk, I show how the standard topics of Gaussian Elimination and Gram-Schmidt can be re-worked using only integers. The material on Gaussian elimination has been developed by many authors, but the Gram-Schmidt process is new.