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"quote": "圆群可以与平面 $\\mathbf { R } ^ { 2 }$ 的旋转群等同；在这种情况下，它称为[特殊正交群(special orthogonal group)](../../../../../concepts/linear-algebra/special-orthogonal-group) $SO(2)$（原因见第 4 章）。不过，将 $\\mathbf { R } ^ { 2 }$ 与复平面 $\\mathbf{C}$ 等同起来，并改用下面这个与 $SO(2)$ 同构的群，会更方便：",
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"quote": "The circle group can be identified with the group of rotations of the plane $\\mathbf { R } ^ { 2 }$; in this form, it is called the [special orthogonal group](../../../../../concepts/linear-algebra/special-orthogonal-group) $SO( 2 )$, for reasons discussed in chapter 4. It is quite convenient, however, to identify $\\mathbf { R } ^ { 2 }$ with the complex plane $\\mathbf{C}$ and work with the following group (which is isomorphic to $SO( 2 )$):\n",
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"quote": "> [!recall]- 回顾：特殊正交群 → [原定义](02-lie-algebras-of-the-orthogonal-and-unitary-groups#concept-5-special-orthogonal-group) \n> - [特殊正交群(special orthogonal group)](../../../../../concepts/linear-algebra/special-orthogonal-group) $SO(n)\\subset SL(n,\\mathbf{R})$ 是 $O(n)$ 中行列式为 $1$ 的子群。它与 $O(n)$ 具有相同的李代数：$\\mathfrak{so}(n)=\\mathfrak{o}(n)$。",
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"quote": "二维平面中绕原点的旋转由[特殊正交群(special orthogonal group)](../../../../../concepts/linear-algebra/special-orthogonal-group) $SO(2)$ 的元素表示。逆时针旋转角度 $\\theta$ 对应的旋转矩阵为：",
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