Matrix exponential via Clifford algebras

Abstract

We use isomorphism $\phi$ between matrix algebras and simple orthogonal Clifford algebras $\cl(Q)$ to compute matrix exponential $e^A$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\phi (A)$ in $\cl(Q),$ where the quadratic form $Q$ has a suitable signature $(p,q),$ is exponentiated modulo a minimal polynomial of $p$ using Clifford exponential. Elements of $\cl(Q)$ are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in $\cl(Q)$ are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given.