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        "quote": "可以从两个角度理解Clifford代数与 $O(n)$ 的关系。第一个角度利用[<u class=\"concept-term\" data-concept-reference=\"concepts/geometry/cartan-dieudonne-theorem\" data-concept-identity=\"urn:uuid:ec5695e9-5589-4bda-bdd1-786f7d96125c\" data-concept-route=\"/concept-identities#concept-ec5695e9-5589-4bda-bdd1-786f7d96125c\" id=\"first-d0e98c2775cd151b9da4-zh\">Cartan–Dieudonné定理(Cartan–Dieudonné theorem)</u>](../../../../../concepts/geometry/cartan-dieudonne-theorem)：任意正交变换都可由至多 $n$ 次超平面反射得到。关于垂直于非零向量 $\\mathbf w$ 的超平面的[<u class=\"concept-term\" data-concept-reference=\"concepts/geometry/orthogonal-reflection\" data-concept-identity=\"urn:uuid:3057bc98-1560-4f68-971f-f741195b6499\" data-concept-route=\"/concept-identities#concept-3057bc98-1560-4f68-971f-f741195b6499\" id=\"first-a01df8be599f2af812c2-zh\">正交反射(orthogonal reflection)</u>](../../../../../concepts/geometry/orthogonal-reflection)，把 $\\mathbf v$ 映为",
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