 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: Hugo RodrŽiguez OrdŽo~nez (University of Regina)
Title: Matrix representation of polynomial multiplications
Date: Friday, October 5, 2007
Time: 3:30
Place: Math & Stats Lounge (CW 307.20)
Abstract
It is known that any linear transformation between finite dimensional
vector spaces can be encoded by means of a matrix. With a few variations,
we can look at the multiplication of two polynomials with real coefficients
as a linear transformation and hence represent it with a matrix containing
the coefficients of either polynomial factor.
The vector space Rm, where m is a power of 2, can be given a multi
plicative structure yielding what are called the CayleyDickson algebras, the
real and complex numbers being the first two examples. I will construct a
matrix representation of the multiplication in CayleyDickson algebras and
then generalise the matrix associated to polynomial multiplication to the
case where the coefficients are in a CayleyDickson algebra.
