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"quote": "> [!example] 例 2.15 \n>\n> 复矩阵 $\\mathsf{A}$ 的伴随矩阵(adjoint)（共轭转置）定义为 $\\mathsf{A}^{\\dagger}=\\overline{\\mathsf{A}^{T}}$，分量为 $a_{ij}^{\\dagger}=\\overline{a_{ji}}$；复数上的横线表示复共轭。若 $n\\times n$ 复矩阵 $\\mathsf{U}$ 满足\n>\n> \n>\n> $$\n> \\mathsf{U}\\mathsf{U}^{\\dagger}=\\mathsf{I},\\tag{2.12}\n> $$\n>\n> 则称它为酉矩阵(unitary matrix)。立即可得\n>\n> $$\n> \\det\\mathsf{U}\\,\\overline{\\det\\mathsf{U}}=|\\det\\mathsf{U}|^{2}=1.\n> $$\n>\n> 因而存在实数 $\\phi\\in[0,2\\pi)$，使 $\\det\\mathsf{U}=e^{i\\phi}$。所有酉矩阵都非奇异，群性质也容易验证。全体 $n\\times n$ 酉矩阵组成$n$ 阶酉群(unitary group)，记作 $U(n)$。其中行列式为 $1$ 的酉矩阵组成$n$ 阶特殊酉群(special unitary group)，记作 $SU(n)$。",
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"quote": "先看单位矩阵：将它乘以 $i\\theta$ 后取指数，得到一个对角的酉矩阵(unitary matrix)：",
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