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"# Latex数学公式\n",
"\n",
"\n",
"用到数学符号总是从其他地方截图，一是看起来不美观，二是总依赖一堆图，还需要网络上去查找，一旦发生变更就更麻烦，索性就看了看手写数学公式的方式，发现也不复杂。于是做个笔记，方便以后查找。\n",
"\n",
"> fuck! github不支持latex，请自行解决观看方式。\n",
"\n",
"## 开始和结束符号\n",
"\n",
"数学公式使用`$`符号包裹，块级公式使用两个`$$`符号，行内元素使用一个`$`符号。\n",
"\n",
"示例：\n",
"\n",
"```\n",
"$$a^2 + b^2 = c^2$$\n",
"这是$a^2 + b^2 = c^2$行内公式\n",
"\n",
"```\n",
"\n",
"效果：\n",
"\n",
"$$a^2 + b^2 = c^2$$\n",
"\n",
"这是$a^2 + b^2 = c^2$行内公式\n",
"\n",
"## 上下标\n",
"\n",
"数学公式中上下标使用比较频繁，上标使用`^`表示，下标使用`_`表示：\n",
"\n",
"```\n",
"$$A^N_K$$\n",
"```\n",
"\n",
"$$A^N_K$$\n",
"\n",
"## 群组\n",
"\n",
"当上下标需要多个元素时，就需要使用`{}`包裹起来：\n",
"\n",
"```\n",
"$$a^{2+1}$$\n",
"```\n",
"\n",
"$$a^{2+1}$$\n",
"\n",
"## 不等式\n",
"\n",
"输入`不等式`时，可以使用专用符号代替，注意需要加前缀`\\`：\n",
"\n",
"```\n",
"$$a\\geq b$$\n",
"$$a\\leq b$$\n",
"$$a\\neq b$$\n",
"```\n",
"$$ a\\geq b$$\n",
"$$a\\leq b$$\n",
"$$a\\neq b$$\n",
"\n",
"## 平方根\n",
"\n",
"```\n",
"$$ \\sqrt[n]\t{x} $$\n",
"$$\\sqrt{1+\\sqrt[^p\\!]{1+a^2}}$$\n",
"```\n",
"$$ \\sqrt[n]\t{x} $$\n",
"$$\\sqrt{1+\\sqrt[^p\\!]{1+a^2}}$$\n",
"\n",
"## 希腊字母\n",
"\n",
"```\n",
"$$ \\lambda \\xi \\pi \\mu \\Phi \\omega \\alpha \\beta \\gamma $$\n",
"```\n",
"\n",
"$$ \\lambda \\\t \\xi \\\t\\pi \\\t\\mu \\\t\\Phi \\\t\\omega \\\t\\alpha \\\t\\beta \\\t\\gamma $$\n",
"\n",
"## 水平线\n",
"\n",
"```\n",
"$$ \\overline{m+n} $$\n",
"$$ \\overbrace{m+n} $$\n",
"$$ \\underbrace{a+b+\\cdots+z} $$\n",
"```\n",
"\n",
"$$ \\overline{m+n} $$\n",
"$$ \\overbrace{m+n} $$\n",
"$$ \\underbrace{a+b+\\cdots+z} $$\n",
"\n",
"\n",
"## 点与省略号\n",
"\n",
"```\n",
"$$ \\cdot $$\n",
"$$ \\cdots$$\n",
"```\n",
"\n",
"$$ \\cdot $$\n",
"$$ \\cdots$$\n",
"\n",
"```\n",
"$$a+b+\\cdots+n$$\n",
"```\n",
"\n",
"$$a+b+\\cdots+n$$\n",
"\n",
"\n",
"## 分子、分母\n",
"\n",
"分子分母表达式使用`\\frac{分子}{分母}`:\n",
"\n",
"```\n",
"$$\\frac{x+y}{2}$$\n",
"$$\\frac{1}{1+\\frac{1}{2}}$$\n",
"```\n",
"$$\\frac{x+y}{2}$$\n",
"$$\\frac{1}{1+\\frac{1}{2}}$$\n",
"\n",
"\n",
"## 向量\n",
"\n",
"```\n",
"$$ \\overrightarrow{AB} $$\n",
"```\n",
"\n",
"$$ \\overrightarrow{AB} $$\n",
"\n",
"\n",
"\n",
"## 求和符号\n",
"\n",
"```\n",
"$$\\sum_{k=1}^{n}\\frac{1}{k}$$\n",
"```\n",
"\n",
"$$\\sum_{k=1}^{n}\\frac{1}{k}$$\n",
"\n",
"\n",
"## 极限\n",
"\n",
"```\n",
"$$ \n",
"\\lim_{m \\to \\infty}\n",
"\\sum_{k=1}^n \\frac{1}{k^2}= \\frac{\\pi^2}{6}\n",
"$$\n",
"```\n",
"\n",
"$$ \n",
"\\lim_{m \\to \\infty}\n",
"\\sum_{k=1}^n \\frac{1}{k^2}= \\frac{\\pi^2}{6}\n",
"$$\n",
"\n",
"\n",
"## 微积分符号\n",
"\n",
"```\n",
"$$\\int_a^b f(x)dx$$\n",
"```\n",
"\n",
"$$\\int_a^b f(x)dx$$\n",
"\n",
"\n",
"## 少于 10 列的矩阵\n",
"\n",
"```\n",
"$$\\begin{matrix}1 & 2\\\\3 &4\\end{matrix}$$\n",
"$$\\begin{pmatrix}1 & 2\\\\3 &4\\end{pmatrix}$$\n",
"$$\\begin{bmatrix}1 & 2\\\\3 &4\\end{bmatrix}$$\n",
"$$\\begin{Bmatrix}1 & 2\\\\3 &4\\end{Bmatrix}$$\n",
"$$\\begin{vmatrix}1 & 2\\\\3 &4\\end{vmatrix}$$\n",
"$$\\begin{Vmatrix}1 & 2\\\\3 &4\\end{Vmatrix}$$\n",
"```\n",
"\n",
"$$\\begin{matrix}1 & 2\\\\3 &4\\end{matrix}$$\n",
"$$\\begin{pmatrix}1 & 2\\\\3 &4\\end{pmatrix}$$\n",
"$$\\begin{bmatrix}1 & 2\\\\3 &4\\end{bmatrix}$$\n",
"$$\\begin{Bmatrix}1 & 2\\\\3 &4\\end{Bmatrix}$$\n",
"$$\\begin{vmatrix}1 & 2\\\\3 &4\\end{vmatrix}$$\n",
"$$\\begin{Vmatrix}1 & 2\\\\3 &4\\end{Vmatrix}$$\n",
"\n",
"\n",
"## 大于 10 列的矩阵\n",
"\n",
"```\n",
"$$\n",
"\\mathbf{X} =\n",
"\\left( \\begin{array}{ccc}\n",
"x_{11} & x_{12} & \\ldots \\\\\n",
"x_{21} & x_{22} & \\ldots \\\\\n",
"\\vdots & \\vdots & \\ddots\n",
"\\end{array} \\right)\n",
"$$\n",
"```\n",
"\n",
"$$\n",
"\\mathbf{X} =\n",
"\\left( \\begin{array}{ccc}\n",
"x_{11} & x_{12} & \\ldots \\\\\n",
"x_{21} & x_{22} & \\ldots \\\\\n",
"\\vdots & \\vdots & \\ddots\n",
"\\end{array} \\right)\n",
"$$\n",
"\n",
"## 矩阵分割线\n",
"\n",
"```\n",
"$$\n",
"\\left(\\begin{array}{c|c}\n",
"1 & 2 \\\\\n",
"\\hline\n",
"3 & 4\n",
"\\end{array}\\right)\n",
"$$\n",
"```\n",
"\n",
"$$\n",
"\\left(\\begin{array}{c|c}\n",
"1 & 2 \\\\\n",
"\\hline\n",
"3 & 4\n",
"\\end{array}\\right)\n",
"$$\n",
"\n",
"## 附录\n",
"\n",
"Greek letters\n",
"\n",
"$$\n",
"\\alpha A\n",
"\\nu N\n",
"\\beta B\n",
"\\xi\\Xi\n",
"\\gamma \\Gamma\n",
"\\delta \\Delta\n",
"\\pi \\Pi\n",
"\\epsilon \\varepsilon E\n",
"\\rho\\varrho P\n",
"\\zeta Z\n",
"\\sigma \\Sigma\n",
"\\eta H\n",
"\\tau T\n",
"\\theta \\vartheta \\Theta\n",
"\\upsilon \\Upsilon\n",
"\\iota I\n",
"\\phi \\varphi \\Phi\n",
"\\kappa K\n",
"\\chi X\n",
"\\lambda \\Lambda\n",
"\\psi \\Psi\n",
"\\mu M\n",
"\\omega \\Omega\n",
"$$\n",
"\n",
"Arrows\n",
"\n",
"$$\n",
"\\leftarrow\n",
"\\Leftarrow\n",
"\\rightarrow\n",
"\\Rightarrow\n",
"\\leftrightarrow\n",
"\\rightleftharpoons\n",
"\\uparrow\n",
"\\downarrow\n",
"\\Uparrow\n",
"\\Downarrow\n",
"\\Leftrightarrow\n",
"\\Updownarrow\n",
"\\mapsto\n",
"\\longmapsto\n",
"\\nearrow\n",
"\\searrow\n",
"\\swarrow\n",
"\\nwarrow\n",
"\\leftharpoonup\n",
"\\rightharpoonup\n",
"\\leftharpoondown\n",
"\\rightharpoondown\n",
"$$\n",
"\n",
"Miscellaneous symbols\n",
"\n",
"$$\n",
"\\infty\n",
"\\forall\n",
"\\Re\n",
"\\Im\n",
"\\nabla\n",
"\\exists\n",
"\\partial\n",
"\\nexists\n",
"\\emptyset\n",
"\\varnothing\n",
"\\wp\n",
"\\complement\n",
"\\neg\n",
"\\cdots\n",
"\\square\n",
"\\surd\n",
"\\blacksquare\n",
"\\triangle\n",
"$$\n",
"\n",
"Binary Operation/Relation Symbols\n",
"\n",
"$$\n",
"\\times\n",
"\\otimes\n",
"\\div\n",
"\\cap\n",
"\\cup\n",
"\\neq\n",
"\\leq\n",
"\\geq\n",
"\\in\n",
"\\perp\n",
"\\notin\n",
"\\subset\n",
"\\simeq\n",
"\\approx\n",
"\\wedge\n",
"\\vee\n",
"\\oplus\n",
"\\otimes\n",
"\\Box\n",
"\\boxtimes\n",
"\\equiv\n",
"\\cong\n",
"$$\n",
"\n"
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