Doust's information pages
Trigonometric identities, linear algebra and computer algebra
Amer. Math. Monthly, 112 (2005), 155-164.
Ian Doust, M.D. Hirschhorn and Jocelyn Ho
Address: School of Mathematics, University of New South Wales, Sydney
NSW 2052, Australia
As the examples in this paper show, many standard identities can be interpreted as
statements about the eigenvalues (or generalized eigenvalues) of a matrix. Once one
has a suitable matrix identity, then elementary linear algebra provides a powerful
technique for extracting new and more complicated identities from old ones.
Our little journey of discovery heavily underlined the power of a modern computer
algebra package in providing inspiration in mathematical investigations.
This paper will appear in the American Mathematical Monthly. The version that appears in
print may differ significantly from the preprint available here.
The preprint (dated 12/11/2004) is available in several forms:
Please contact Ian if you have any trouble downloading the files.