Date of Award

5-2011

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Committee Chair

John Perry

Committee Chair Department

Mathematics

Abstract

Given a matrix of integers, we wish to compute the determinant using a method that does not introduce fractions. Fraction-Free Triangularization, Bareiss’ Algorithm (based on Sylvester’s Identity) and Dodgson’s Method (based on Jacobi’s Theorem) are three such methods. However, both Bareiss’ Algorithm and Dodgson’s Method encounter division by zero for some matrices. Although there is a well-known workaround for the Bareiss Algorithm that works for all matrices, the workarounds that have been developed for Dodgson’s method are somewhat difficult to apply and still fail to resolve the problem completely. After investigating new workarounds for Dodgson’s Method, we give a modified version of the old method that relies on a well-known property of determinants to allow us to compute the determinant of any integer matrix.

Included in

Mathematics Commons

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