# 画矩阵需要用到特殊的语法
（1）画普通矩阵，不带括号的
$$
\begin{matrix}
a & b & c & d & e\\
f & g & h & i & j \\
k & l & m & n & o \\
p & q & r & s & t
\end{matrix}
$$
```
\begin{matrix} a & b & c & d & e\\ f & g & h & i & j \\ k & l & m & n & o \\ p & q & r & s & t \end{matrix}
```
（2）画带中括号的矩阵
$$
\left[
\begin{matrix}
a & b & c & d & e\\
f & g & h & i & j \\
k & l & m & n & o \\
p & q & r & s & t
\end{matrix}
\right]
$$
```
\left[ \begin{matrix} a & b & c & d & e\\ f & g & h & i & j \\ k & l & m & n & o \\ p & q & r & s & t \end{matrix} \right]
```
(3) 画带大括号的矩阵
$$
\left\{
\begin{matrix}
a & b & c & d & e\\
f & g & h & i & j \\
k & l & m & n & o \\
p & q & r & s & t
\end{matrix}
\right\}
$$
```
\left\{ \begin{matrix} a & b & c & d & e\\ f & g & h & i & j \\ k & l & m & n & o \\ p & q & r & s & t \end{matrix} \right\}
```
（4）矩阵前加个参数
$$A=
\left\{
\begin{matrix}
a & b & c & d & e\\
f & g & h & i & j \\
k & l & m & n & o \\
p & q & r & s & t
\end{matrix}
\right\}
$$
```
A= \left\{ \begin{matrix} a & b & c & d & e\\ f & g & h & i & j \\ k & l & m & n & o \\ p & q & r & s & t \end{matrix} \right\}
```
（5）矩阵中间有省略号
//\cdots为水平方向的省略号
//\vdots为竖直方向的省略号
//\ddots为斜线方向的省略号
$$A=
\left\{
\begin{matrix}
a & b & \cdots & e\\
f & g & \cdots & j \\
\vdots & \vdots & \ddots & \vdots \\
p & q & \cdots & t
\end{matrix}
\right\}
$$
```
A= \left\{ \begin{matrix} a & b & \cdots & e\\ f & g & \cdots & j \\ \vdots & \vdots & \ddots & \vdots \\ p & q & \cdots & t \end{matrix} \right\}
```
（6）矩阵中间加根横线
//array必须为array
//{cccc|c}中的c表示矩阵元素，可以控制|的位置
$$A=
\left\{
\begin{array}{cccc|c}
a & b & c & d & e\\
f & g & h & i & j \\
k & l & m & n & o \\
p & q & r & s & t
\end{array}
\right\}
$$
```
A= \left\{ \begin{array}{cccc|c} a & b & c & d & e\\ f & g & h & i & j \\ k & l & m & n & o \\ p & q & r & s & t \end{array} \right\}
```
# 求和的公式表达
内嵌公式，使用```$...$```. 单独展示的一行使用 ```$$...$$```.
渲染的差别，比如
$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
会显示$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$ (内嵌模式) ，而下面这样
$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$
为独立的一块渲染区域，它是居中展示的，字体也要更大一些
# 符号
__希腊字母__,
```\alpha, \beta, …, \omega```: $\alpha, \beta, … \omega$.
__大写__,
```\Gamma, \Delta, …, \Omega```: $\Gamma, \Delta, …, \Omega$.
__上标和下标__,
use ^ and _. For example, ```x_i^2```: $x_i^2$, ```\log_2 x```: $\log_2 x$.
__分组__
Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {…}.
If you do __10^10__, you will get a surprise: $10^10$.
But __10^{10}__ gives what you probably wanted: $10^{10}$.
Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error;
{x^y}^z is ${x^y}^z$, and x^{y^z} is $x^{y^z}$. Observe the difference between x_i^2 $x_i^2$ and x_{i^2} $x_{i^2}$.
__Parentheses(圆括号)__
一般的()[]， $(2+3)[4+4]$. Use `\{ and \}` for curly braces $\{\}$.
These do not scale with the formula in between, so if you write `(\frac{\sqrt x}{y^3})` the parentheses will be too small: (x√y3)
. Using `\left(…\right)` will make the sizes adjust automatically to the formula they enclose: $\left(\frac{\sqrt x}{y^3}\right)$ .
`\left` and `\right` apply to all the following sorts of parentheses:
|synbol|means|
|----|----|
| `( and )` | $$\left( x \right)$$ |
| `[ and ]` | $$\left[ x \right]$$ |
| `\{ and \}` | $$ \left\{ x \right\} $$ |
| `\|` | $$\left\| x \right\|$$ |
| `\vert , \Vert` | $$\|x\|$$ 有问题，可能需要在其他的语境下才生效|
| `\langle and \rangle` | $$\langle x \rangle$$|
| `\lceil and \rceil` | $$\lceil x \rceil $$ |
| `\lfloor and \rfloor` | $$\lfloor x \rfloor $$|
. \middle can be used to add additional dividers. There are also invisible parentheses, denoted by `.` :
`\left. \frac12\right\rbrace` is $$\left.\frac12\right\rbrace$$ .
If manual size adjustments are required: ` \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) ` gives $$ \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) $$ .
Sums and integrals `\sum and \int`; the subscript is the lower limit and the superscript is the upper limit, so for example `\sum_1^n` $\sum_1^n$. Don't forget `{…}` if the limits are more than a single symbol. For example,
``` \sum_{i=0}^\infty i^2``` is $\sum_{i=0}^\infty i^2 $.
Similarly,
|symbol|redered as|
|--|--|
|`\prod` | $\prod$ |
| `\int ` | $\int$ |
| `\bigcup ` | $\bigcup$ |
| `\bigcap ` | $\bigcap$ |
| `\iint ` | $\iint$ |
| `\iiint` | $\iiint$ |
| `\idotsint` | $\idotsint$ |
.
__Fractions__ There are three ways to make these. `\frac ab` applies to the next two groups, and produces $\frac ab$ ;
for more complicated numerators and denominators use `{…}`: `\frac{a+1}{b+1}` is $\frac{a+1}{b+1}$.
If the numerator and denominator are complicated, you may prefer `\over`, which splits up the group that it is in: `{a+1\over b+1}` is ${a+1\over b+1}$ .
Using `\cfrac{a}{b}` command is useful for continued fractions $\cfrac{a}{b}$ , more details for which are given in this sub-article.
Fonts
Use \mathbb or \Bbb for "blackboard bold": ℂℍℕℚℝℤ
|symbols | for| redered as |
|--|--|--|
| `\mathbf` | boldface | $\mathbf ABCDEFGHIJKLMNOPQRSTUVWXYZ$ |
| `\mathit` | italics| $\mathit ABCDEFGHIJKLMNOPQRSTUVWXYZ$ , $\mathit abcdefghijklmnopqrstuvwxyz$ |
|`\pmb` | boldfaced italics | $\pmb ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ$ $\pmb abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz$ |
| `\mathtt` | typewriter | $\mathtt ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ$ |
| `\mathrm` | roman | $mathrm abcdefghijklmnopqrstuvwxyz$ |
| `\mathsf` | sans-serif | $\mathsf ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ$ |
| `\mathcal` | calligraphic letters| $\mathcal ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ$|
| `\mathscr` | script letters | $\mathscr ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ$ |
| `\mathfrak` | Fraktur (old German style) letters| $\mathfrak ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ$ |
---------------------------------
----------------------------
* Radical signs Use sqrt,
which adjusts to the size of its argument:`\sqrt{x^3} x3` means: $\sqrt{x^3} x3$;
`\sqrt[3]{\frac xy}` means: $\sqrt[3]{\frac xy}$ .
For complicated expressions, consider using {...}^{1/2} instead.
* Some special functions such as "lim", "sin", "max", "ln", and so on are normally set in roman font instead of italic font.
Use \lim, \sin, etc. to make these: `\sin x`:$\sin x$ , not `sin x` : $sin x$.
Use subscripts to attach a notation to \lim: `\lim_{x\to 0}`: $\lim_{x\to 0}$
# There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:
| symbols | redered as |
|--|--|
| ` \lt \gt \le \leq \leqq \leqslant \ge \geq \geqq \geqslant \neq ` | $\lt \gt \le \leq \leqq \leqslant \ge \geq \geqq \geqslant \neq $ |
| You can use \not to put a slash through almost anything: `\not\lt` | $\not\lt$ but it often looks bad |
|`\times \div \pm \mp` | $\times \div \pm \mp$.|
| `\cdot` is a centered dot | $x \cdot y$ |
| `\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing ` | $\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing$ |
| `{n+1 \choose 2k} or \binom{n+1}{2k} (n+12k)` | ${n+1 \choose 2k} or \binom{n+1}{2k} (n+12k)$ |
| `\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto` | $\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto$ |
| `\land \lor \lnot \forall \exists \top \bot \vdash \vDash` | $\land \lor \lnot \forall \exists \top \bot \vdash \vDash$ |
| `\star \ast \oplus \circ \bullet` | $\star \ast \oplus \circ \bullet $ |
| `\approx \sim \simeq \cong \equiv \prec \lhd \therefore` | $\approx \sim \simeq \cong \equiv \prec \lhd \therefore $ |
| `\infty \aleph_0` | $\infty \aleph_0$ |
| ` \nabla \partial` | $\nabla \partial$ |
* For modular equivalence, use \pmod like this: `a\equiv b\pmod n` $$a\equiv b\pmod n$$.
* `\ldots` is the dots in a1,a2,…,an
* `\cdots` is the dots in a1+a2+…+an
* Some Greek letters have variant forms:
`\epsilon \varepsilon `: $\epsilon \varepsilon$,
`\phi \varphi`: $\phi \varphi$,
and others.
Script lowercase l is `\ell` $\ell$ .
Detexify lets you draw a symbol on a web page and then lists the TEX symbols that seem to resemble it.
__These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains a list of currently supported LATEX commands, and one can also check Dr. Carol JVF Burns's page of TEX Commands Available in MathJax.__
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