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  "body": "\n## Statement\n\nLet $V$ be a real inner product space of finite dimension $n$.\nThen each linear isometry $T \\colon V \\to V$ is a composition of at most $n$ [[reflections|06BRDF3F0E]] in hyperplanes of $V$.\n\n## Remarks\n\nThe identity map is the composition of zero reflections.\nIn $\\R^2$, each rotation is the composition of two reflections in lines through the origin.\nThe theorem holds more generally for nondegenerate symmetric bilinear forms on spaces over fields of characteristic not $2$.\n\n## Explanations\n\n### L1 human\n\nEvery rigid linear motion of $n$-dimensional space is a sequence of at most $n$ mirror reflections.\nSo reflections are the building blocks of all isometries.\nIn the plane, a rotation by $\\theta$ is the product of two reflections in lines at the angle $\\theta/2$.\n",
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