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Matrix exponential via Clifford algebras

Rafal Ablamowicz
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Abstract

We use isomorphism $\varphi$ 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 $p=\varphi(A)$ 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.

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Rafal Ablamowicz. 1998-07-01. Matrix exponential via Clifford algebras. https://doi.org/10.2991/jnmp.1998.5.3.5

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