Matrix Exponential via Clifford Algebras

DOI

10.2991/jnmp.1998.5.3.5How to use a DOI?

Abstract

We use isomorphism 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 = (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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Rafał Abłamowicz
PY  - 1998
DA  - 1998/08/01
TI  - Matrix Exponential via Clifford Algebras
JO  - Journal of Nonlinear Mathematical Physics
SP  - 294
EP  - 313
VL  - 5
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1998.5.3.5
DO  - 10.2991/jnmp.1998.5.3.5
ID  - Abłamowicz1998
ER  -