Matrix Exponential via Clifford Algebras

Abstract

Expanded version of a talk presented at the Special Session on ‘Octonions and Clifford Algebras’, 1997 Spring Western Sectional 921st Meeting of the American Mathematical Society, Oregon State University, Corvallis, OR, 19–20 April 1997. We use isomorphism ϕ between matrix algebras and simple orthogonal Clifford algebras C (Q) to compute matrix exponential eA of a real, complex, and quaternionic matrix A. The isomorphic image p = ϕ(A) in C (Q), where the quadratic form Q has a suitable signature (p, q), is exponentiated modulo a minimal polynomial of p using Clifford exponential. Elements of C (Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in C (Q) are performed with a Maple package ‘CLIFFORD’. Three examples of matrix exponentiation are given.