Approximating the square root and logarithm functions in Clifford algebras: what to do in the case of negative eigenvalues?

Dr Paul Leopardi (ANU)

MSI Computational Mathematics Seminar Series

DATE: 2010-05-31
TIME: 16:00:00 - 17:00:00
LOCATION: G35 John Dedman Building
CONTACT: JavaScript must be enabled to display this email address.

ABSTRACT:
Functions in Clifford algebras are a special case of matrix functions, as can be seen via representation theory. The square root and logarithm functions pose problems for the author of a general purpose library of Clifford algebra functions, partly because the principal square root and principal logarithm of a matrix do not exist for a matrix containing a negative eigenvalue. We are thus led to the following problems: 1. Define the square root and logarithm of a multivector in the case where the matrix representation has negative eigenvalues. 2. Predict or detect negative eigenvalues.

Demo: GluCat: Clifford algebra template library for C++ PyCliCal: Clifford algebra calculator extension to Python, based on GluCat.

BIO:
http://gan.anu.edu.au/~leopardi/