Matrix exponential via Clifford algebras
Rafal Ablamowicz
Abstract
We use isomorphism φ between matrix algebras and simple orthogonal Clifford algebras (Q) to compute matrix exponential eA of a real, complex, and quaternionic matrix A. The isomorphic image p=φ(A) in (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 (Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in (Q) are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given.
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