{"paper":{"title":"Matrix exponential via Clifford algebras","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Rafal Ablamowicz","submitted_at":"1998-07-01T00:00:00Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9807038","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}