A
B
⃗
A
B
→
\vec{AB} \qquad \overrightarrow{AB}
ABAB
$\underbrace{\overbrace{(a+b+c)}^6 \cdot \overbrace{(d+e+f)}^7} _\text{meaning of life} = 42$
(
a
+
b
+
c
)
⏞
6
⋅
(
d
+
e
+
f
)
⏞
7
⏟
meaning of life
=
42
\underbrace{\overbrace{(a+b+c)}^6 \cdot \overbrace{(d+e+f)}^7} _\text{meaning of life} = 42
meaning of life(a+b+c)6⋅(d+e+f)7=42
箭头
$$ a\xleftarrow{x+y+z} b $$
a
←
x
+
y
+
z
b
a\xleftarrow{x+y+z} b
ax+y+zb
$$ c\xrightarrow[x<y]{a*b*c}d $$
c
→
x
<
y
a
∗
b
∗
c
d
c\xrightarrow[x<y]{a*b*c}d
ca∗b∗cx<yd
括号和定界符
${a,b,c} \neq \{a,b,c\}$
a
,
b
,
c
≠
{
a
,
b
,
c
}
{a,b,c} \neq \{a,b,c\}
a,b,c={a,b,c}
$$\begin{aligned}
a + b + c + d + e + f + g + h + i \\
= j + k + l + m + n\\
= o + p + q + r + s\\
= t + u + v + x + z
\end{aligned}$$
a
+
b
+
c
+
d
+
e
+
f
+
g
+
h
+
i
=
j
+
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+
m
+
n
=
o
+
p
+
q
+
r
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s
=
t
+
u
+
v
+
x
+
z
\begin{aligned} a + b + c + d + e + f + g + h + i \\ = j + k + l + m + n\\ = o + p + q + r + s\\ = t + u + v + x + z \end{aligned}
a+b+c+d+e+f+g+h+i=j+k+l+m+n=o+p+q+r+s=t+u+v+x+z
多行公式
$$\begin{aligned}
a & = b + c \\
& = d + e
\end{aligned}$$
a
=
b
+
c
=
d
+
e
\begin{aligned} a & = b + c \\ & = d + e \end{aligned}
a=b+c=d+e
$$\begin{aligned}
a ={} & b + c \\
={} & d + e + f + g + h + i + j + k + l \\
& + m + n + o \\
={} & p + q + r + s
\end{aligned}$$
a
=
b
+
c
=
d
+
e
+
f
+
g
+
h
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i
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k
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o
=
p
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q
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r
+
s
\begin{aligned} a = & b + c \\ = & d + e + f + g + h + i + j + k + l \\ & + m + n + o \\ = & p + q + r + s \end{aligned}
a===b+cd+e+f+g+h+i+j+k+l+m+n+op+q+r+s
$$\begin{aligned}
a &=1 & b &=2 & c &=3 \\
d &=-1 & e &=-2 & f &=-5
\end{aligned}$$
a
=
1
b
=
2
c
=
3
d
=
−
1
e
=
−
2
f
=
−
5
\begin{aligned} a &=1 & b &=2 & c &=3 \\ d &=-1 & e &=-2 & f &=-5 \end{aligned}
ad=1=−1be=2=−2cf=3=−5
默认右对齐？
$$\begin{aligned}
a = b + c \\
d = e + f + g \\
h + i = j + k \\
l + m = n
\end{aligned}$$
a
=
b
+
c
d
=
e
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f
+
g
h
+
i
=
j
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k
l
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m
=
n
\begin{aligned} a = b + c \\ d = e + f + g \\ h + i = j + k \\ l + m = n \end{aligned}
a=b+cd=e+f+gh+i=j+kl+m=n
左对齐：
$$\begin{aligned}
&a = b + c \\
&d = e + f + g \\
&h + i = j + k \\
&l + m = n
\end{aligned}$$
a
=
b
+
c
d
=
e
+
f
+
g
h
+
i
=
j
+
k
l
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m
=
n
\begin{aligned} &a = b + c \\ &d = e + f + g \\ &h + i = j + k \\ &l + m = n \end{aligned}
a=b+cd=e+f+gh+i=j+kl+m=n
公用编号的多行公式
公式环境用等号对齐：
$$
\begin{aligned}
a &= b + c \\
d &= e + f + g \\
h + i &= j + k \\
l + m &= n
\end{aligned} \tag{1.3}
$$
a
=
b
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c
d
=
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+
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g
h
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i
=
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m
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n
(1.3)
\begin{aligned} a &= b + c \\ d &= e + f + g \\ h + i &= j + k \\ l + m &= n \end{aligned} \tag{1.3}
adh+il+m=b+c=e+f+g=j+k=n(1.3)
X
=
(
x
11
x
12
…
x
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n
x
21
x
22
…
x
2
n
⋮
⋮
⋱
⋮
x
n
1
x
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2
…
x
n
n
)
\mathbf{X} = \left( \begin{array}{cccc} x_{11} & x_{12} & \ldots & x_{1n}\\ x_{21} & x_{22} & \ldots & x_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ x_{n1} & x_{n2} & \ldots & x_{nn}\\ \end{array} \right)
X=⎝⎜⎜⎜⎛x11x21⋮xn1x12x22⋮xn2……⋱…x1nx2n⋮xnn⎠⎟⎟⎟⎞
$$
|x| = \left\{
\begin{array}{rl}
-x & \text{if } x < 0,\\
0 & \text{if } x = 0,\\
x & \text{if } x > 0.
\end{array} \right.
$$
∣
x
∣
=
{
−
x
if
x
<
0
,
0
if
x
=
0
,
x
if
x
>
0.
|x| = \left\{ \begin{array}{rl} -x & \text{if } x < 0,\\ 0 & \text{if } x = 0,\\ x & \text{if } x > 0. \end{array} \right.
∣x∣=⎩⎨⎧−x0xif x<0,if x=0,if x>0.
$$
|x| = \begin{cases}
-x & \text{if } x < 0,\\
0 & \text{if } x = 0,\\
x & \text{if } x > 0.
\end{cases}
$$
∣
x
∣
=
{
−
x
if
x
<
0
,
0
if
x
=
0
,
x
if
x
>
0.
|x| = \begin{cases} -x & \text{if } x < 0,\\ 0 & \text{if } x = 0,\\ x & \text{if } x > 0. \end{cases}
∣x∣=⎩⎪⎨⎪⎧−x0xif x<0,if x=0,if x>0.
[
x
11
x
12
…
x
1
n
x
21
x
22
…
x
2
n
⋮
⋮
⋱
⋮
x
n
1
x
n
2
…
x
n
n
]
\begin{bmatrix} x_{11} & x_{12} & \ldots & x_{1n}\\ x_{21} & x_{22} & \ldots & x_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ x_{n1} & x_{n2} & \ldots & x_{nn}\\ \end{bmatrix}
⎣⎢⎢⎢⎡x11x21⋮xn1x12x22⋮xn2……⋱…x1nx2n⋮xnn⎦⎥⎥⎥⎤
H
=
[
∂
2
f
∂
x
2
∂
2
f
∂
x
∂
y
∂
2
f
∂
x
∂
y
∂
2
f
∂
y
2
]
\mathbf{H}= \begin{bmatrix} \dfrac{\partial^2 f}{\partial x^2} & \dfrac{\partial^2 f} {\partial x \partial y} \\[8pt] \dfrac{\partial^2 f} {\partial x \partial y} & \dfrac{\partial^2 f}{\partial y^2} \end{bmatrix}
H=⎣⎢⎢⎡∂x2∂2f∂x∂y∂2f∂x∂y∂2f∂y2∂2f⎦⎥⎥⎤
H
=
[
∂
2
f
∂
x
2
∂
2
f
∂
x
∂
y
∂
2
f
∂
x
∂
y
∂
2
f
∂
y
2
]
\mathbf{H}= \begin{bmatrix} \dfrac{\partial^2 f}{\partial x^2} & \dfrac{\partial^2 f} {\partial x \partial y} \\[8pt] \dfrac{\partial^2 f} {\partial x \partial y} & \dfrac{\partial^2 f}{\partial y^2} \end{bmatrix}
H=⎣⎢⎢⎡∂x2∂2f∂x∂y∂2f∂x∂y∂2f∂y2∂2f⎦⎥⎥⎤
公式中的间距
一个常见的用途是修正积分的被积函数 f(x) 和微元 dx 之间的距离。注意微元里的 d 用的 是直立体：
∫
a
b
f
(
x
)
d
x
∫
a
b
f
(
x
)
d
x
\int_a^b f(x)\mathrm{d}x \qquad \int_a^b f(x)\,\mathrm{d}x
∫abf(x)dx∫abf(x)dx
$$\begin{aligned}
\int\int f(x)g(y)
\,\mathrm{d} x\,\mathrm{d} y \\
\int\!\!\!\int
f(x)g(y) \,\mathrm{d} x \,\mathrm{d} y \\
\iint f(x)g(y) \,\mathrm{d} x \,\mathrm{d} y \\
\oint\quad \iint\quad \iiint\quad
\end{aligned}$$
∫
∫
f
(
x
)
g
(
y
)
d
x
d
y
∫
∫
f
(
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)
g
(
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)
d
x
d
y
∬
f
(
x
)
g
(
y
)
d
x
d
y
∮
∬
∭
\begin{aligned} \int\int f(x)g(y) \,\mathrm{d} x\,\mathrm{d} y \\ \int\!\!\!\int f(x)g(y) \,\mathrm{d} x \,\mathrm{d} y \\ \iint f(x)g(y) \,\mathrm{d} x \,\mathrm{d} y \\ \oint\quad \iint\quad \iiint\quad \end{aligned}
∫∫f(x)g(y)dxdy∫∫f(x)g(y)dxdy∬f(x)g(y)dxdy∮∬∭
R
R
R
\mathcal{R} \quad \mathfrak{R} \quad \mathbb{R}
RRR
L
=
−
1
4
F
μ
ν
F
μ
ν
\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}
L=−41FμνFμν
s
u
(
2
)
\mathfrak{su}(2)
su(2) and
s
o
(
3
)
\mathfrak{so}(3)
so(3) Lie algebra
加粗的数学符号
$\mu, M \qquad \boldsymbol{\mu}, \boldsymbol{M}$
μ
,
M
μ
,
M
\mu, M \qquad \boldsymbol{\mu}, \boldsymbol{M}
μ,Mμ,M
r
=
∑
i
=
1
n
(
x
i
−
x
)
(
y
i
−
y
)
[
∑
i
=
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n
(
x
i
−
x
)
2
∑
i
=
1
n
(
y
i
−
y
)
2
]
1
/
2
r = \frac {\sum_{i=1}^n (x_i- x)(y_i- y)} {\displaystyle \left[ \sum_{i=1}^n (x_i-x)^2 \sum_{i=1}^n (y_i-y)^2 \right]^{1/2} }
r=[i=1∑n(xi−x)2i=1∑n(yi−y)2]1/2∑i=1n(xi−x)(yi−y)
其他
证明（因为，所以）
$$\because a \ge b \\ b \ge c \\ \therefore a \ge c$$
∵
a
≥
b
b
≥
c
∴
a
≥
c
\because a \ge b \\ b \ge c \\ \therefore a \ge c
∵a≥bb≥c∴a≥c
如果使用aligned环境，排版效果会好一些
$$\begin{aligned}
\because a \ge b \\ b \ge c \\ \therefore a \ge c
\end{aligned}$$
∵
a
≥
b
b
≥
c
∴
a
≥
c
\begin{aligned} \because a \ge b \\ b \ge c \\ \therefore a \ge c \end{aligned}
∵a≥bb≥c∴a≥c
