Fractionfree Linear Algebra
David Jeffrey djeffrey@uwo.ca
Applied Mathematics University Western Ontario Canada
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 fractionfree
or square root free. In this talk, I show how the standard topics of Gaussian
Elimination and GramSchmidt can be reworked using only integers. The material
on Gaussian elimination has been developed by many authors, but the GramSchmidt
process is new.
