Matrix Exponential via Clifford Algebras
Rafał Abłamowicz · Journal of Nonlinear Mathematical Physics · 1998
We use isomorphism ϕ 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 = ϕ(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.