LaTeX数学符号速查表

Recently, while reading The Dragon Book DX12, I’ve been using LaTeX to document some formulas. To facilitate searching, I’ve compiled a table of commonly used LaTeX mathematical symbols syntax. More symbols can be found at LaTeX:Symbols.

Addition, Subtraction, Multiplication, and Division

Add Syntax Subtract Syntax Multiply Syntax Divide Syntax
$+$ + $-$ - $\times$ \times $\div$ \div

Power Operations

Symbol Syntax Symbol Syntax Symbol Syntax Symbol Syntax
$a^x$ a^x $a^{xyz}$ a^{xyz} $\sqrt{x}$ \sqrt{x} $\sqrt[n]{x}$ \sqrt[n]{x}

Logical Operations

XOR Syntax OR Syntax AND Syntax
$\oplus$ \oplus $\vee$ \vee $\wedge$ \wedge

Absolute Value

Directly insert vertical bars | to specify the vertical length of the bars using \left and \right tags.

$\left| \sum_i \vec{v}_i \left|\Delta t_i\right| \right|$

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Code: \left| \sum_i \vec{v}_i \left|\Delta t_i\right| \right|

Fractions

Refer to the “Fraction” section below for more details on the syntax.

$(\frac{a}{x} )^2$ Syntax: (\frac{a}{x} )^2

The effect of the above expression is: the superscript on the right is not aligned, so it can be improved:

$\left(\frac{a}{x} \right)^2$ Syntax: \left(\frac{a}{x} \right)^2

Other Operations

For details, see the following section.

Sum Syntax Integral Syntax Integral Syntax Product Syntax
$\sum$ \sum $\int$ \int $\oint$ \oint $\prod$ \prod

Relations

Symbol Syntax Symbol Syntax Symbol Syntax Symbol Syntax
$=$ = $\not=$ \not= $\approx$ \approx $\equiv$ \equiv
$<$ < $>$ > $\le$ \le $\ge$ \ge
$\ll$ \ll $\gg$ \gg

Sets

Symbol Syntax Symbol Syntax
$\in$ \in $\ni$ \ni
$\subset$ \subset $\supset$ \supset
$\subseteq$ \subseteq $\supseteq$ \supseteq

Existence

Symbol Syntax Symbol Syntax
$\exists$ \exists $\forall$ \forall

Greek Letters

Directly input according to spelling, there are 22 lowercase and 8 uppercase: uppercase has the first letter of lowercase syntax capitalized. Not all are listed.

Symbol Syntax Symbol Syntax Symbol Syntax
Lowercase $\alpha$ \alpha $\beta$ \beta $\gamma$ \gamma
Uppercase $\Phi$ \Phi $\Omega$ \Omega $\Delta$ \Delta

Arrows

Symbol Syntax Symbol Syntax Symbol Syntax Symbol Syntax Symbol Syntax
$\gets$ \gets $\to$ \to $\Leftarrow$ \Leftarrow $\Rightarrow$ \Rightarrow $\Leftrightarrow$ \Leftrightarrow

Ellipsis

Symbol Syntax Symbol Syntax
$\dots$ \dots $\cdots$ \cdots

Accents

Symbol Syntax Symbol Syntax Symbol Syntax
$\hat{x}$ \hat{x} $\bar{x}$ \bar{x} $\vec{x}$ \vec{x}
$\dot{x}$ \dot{x} $\ddot{x}$ \ddot{x}

Standard Parentheses

Symbol Syntax Symbol Syntax Symbol Syntax Symbol Syntax
$($ ( $)$ ) $[$ [ $]$ ]

Floor and Ceiling Functions

Symbol Syntax Symbol Syntax
$\lfloor$ \lfloor $\rfloor$ \rfloor
$\lceil$ \lceil $\rceil$ \rceil

Spaces

LaTeX omits spaces by default; to input spaces, you must enter commands yourself. mu is a mathematical unit.

Effect Description Syntax
$a \quad b$ Space width is current character width (18mu) \quad
$a , b$ Space width is 3mu ,
$a : b$ Space width is 4mu :
$a ; b$ Space width is 5mu ;
$a ! b$ Space width is -3mu (shrinks left) !
$a \ b$ Space width is standard space key effect Type a space after \
$a \qquad b$ Space width is 36mu \qquad

Superscripts and Subscripts

Use {..} to indicate the positions of superscripts and subscripts to MathJax.

Symbol Syntax Symbol Syntax
$2^2$ 2^2 $a_i$ a_i
$2^{23}$ 2^{23} $n_{i-1}$ n_{i-1}
$a^{i+1}_3$ a^{i+1}_3 $x^{3^2}$ x^{3^2}
$2^{a_i}$ 2^{a_i} $2^a_i$ 2^a_i

Overline and Underline

Over Syntax Under Syntax
$\overline{a+bi}$ \overline{a+bi} $\underline{431}$ \underline{431}

Fractions

There are two sizes: frac and dfrac

Smaller Size Suitable for Print Medium Size Used for Display
Symbol Syntax Symbol Syntax
$\frac{1}{2}$ \frac{1}{2} $\dfrac{1}{2}$ \dfrac{1}{2}
$\frac{2}{x+2}$ \frac{2}{x+2} $\dfrac{2}{x+2}$ \dfrac{2}{x+2}
$\frac{1+\frac{1}{x}}{3x + 2}$ \frac{1+\frac{1}{x}}{3x + 2} $\dfrac{1+\frac{1}{x}}{3x + 2}$ \dfrac{1+\frac{1}{x}}{3x + 2}

Using consecutively (nested): \cfrac

Symbol Syntax
$\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}$ \cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}

Radical Expressions

Symbol Syntax Symbol Syntax
$\sqrt(2)$ \sqrt(2) $\sqrt{2}$ \sqrt{2}
$\sqrt{x+y}$ \sqrt{x+y} $\sqrt{x+\frac{1}{2}}$ \sqrt{x+\frac{1}{2}}
$\sqrt[3]{3}$ \sqrt[3]{3} $\sqrt[n]{x}$ \sqrt[n]{x}

Summation, Product, Limit

Symbol Syntax
$\sum_{i=1}^{\infty}\frac{1}{i}$ \sum_{i=1}^{\infty}\frac{1}{i}
$\prod_{n=1}^5\frac{n}{n-1}$ \prod_{n=1}^5\frac{n}{n-1}
$\lim_{x\to\infty}\frac{1}{x}$ \lim_{x\to\infty}\frac{1}{x}

Differentiation and Partial Derivatives

Symbol Syntax
$\frac{d}{dx}\left(x^2\right) = 2x$ \frac{d}{dx}\left(x^2\right) = 2x
$\int 2x,dx = x^2+C$ \int 2x,dx = x^2+C
$\frac{\partial^2U}{\partial x^2} + \frac{\partial^2U}{\partial y^2}$ \frac{\partial^2U}{\partial x^2} + \frac{\partial^2U}{\partial y^2}

Modulus

$9\equiv 3 \pmod{6}$ —— Syntax: 9\equiv 3 \pmod{6}

Trigonometric Functions

Directly input normally written symbols; not all are listed.

Cosine Syntax Arccosine Syntax Hyperbolic Cosine Syntax
$\cos$ \cos $\arccos$ \arccos $\cosh$ \cosh
Symbol Syntax
$\cos^2 x +\sin^2 x = 1$ \cos^2 x +\sin^2 x = 1
$\cos 90^\circ = 0$ \cos 90^\circ = 0

Matrices

Use $$\begin{matrix}…\end{matrix}$$, and end each row with \\ (in markdown, writing LaTeX double backslashes \\ will be escaped, so use \\\\). Separate matrix elements with &.

$$
\begin{equation}
H_x=\frac{1}{3}\times{
\left[ \begin{array}{ccc}
1 & 0 & -1\\
1 & 0 & -1\\
1 & 0 & -1
\end{array}
\right ]},
H_y=\frac{1}{3}\times{
\left[ \begin{array}{ccc}
1 & 1 & 1\\
0& 0 & 0\\
1 & 1 & 1
\end{array}
\right ]}
\end{equation}
$$

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\begin{equation}
H_x=\frac{1}{3}\times{
\left[ \begin{array}{ccc}
1 & 0 & -1\\\\
1 & 0 & -1\\\\
1 & 0 & -1
\end{array}
\right ]},
H_y=\frac{1}{3}\times{
\left[ \begin{array}{ccc}
1 & 1 & 1\\\\
0& 0 & 0\\\\
1 & 1 & 1
\end{array}
\right ]}
\end{equation}

Matrix with Ellipses

$$
\begin{equation}
S
=\begin{bmatrix}
A & B & \cdots\ &C\\
D & E & \cdots\ & F\\
\vdots & \vdots & \ddots & \vdots \\
G & H & \cdots\ & I\\
\end{bmatrix}
\end{equation}
$$

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9
\begin{equation}
S
=\begin{bmatrix}
A & B & \cdots\ &C\\\\
D & E & \cdots\ & F\\\\
\vdots & \vdots & \ddots & \vdots \\\\
G & H & \cdots\ & I\\\\
\end{bmatrix}
\end{equation}
Vertical Direction Syntax Horizontal Direction Syntax Diagonal Direction Syntax
$\vdots$ \vdots $\cdots$ \cdots $\ddots$ \ddots

matrix

$$
\begin{matrix}
A & B & \cdots\ &C\\
D & E & \cdots\ & F
\end{matrix}
$$

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\begin{matrix}
A & B & \cdots\ &C\\\\
D & E & \cdots\ & F
\end{matrix}

pmatrix

$$
\begin{equation}
S
=\begin{pmatrix}
A & B & \cdots\ &C\\
D & E & \cdots\ & F
\end{pmatrix}
\end{equation}
$$

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\begin{equation}
S
=\begin{pmatrix}
A & B & \cdots\ &C\\\\
D & E & \cdots\ & F
\end{pmatrix}
\end{equation}

bmatrix

$$
\begin{equation}
S
=\begin{bmatrix}
A & B & \cdots\ &C\\
D & E & \cdots\ & F
\end{bmatrix}
\end{equation}
$$

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\begin{equation}
S
=\begin{bmatrix}
A & B & \cdots\ &C\\\\
D & E & \cdots\ & F
\end{bmatrix}
\end{equation}

Bmatrix

$$
\begin{equation}
S
=\begin{Bmatrix}
A & B & \cdots\ &C\\
D & E & \cdots\ & F
\end{Bmatrix}
\end{equation}
$$

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\begin{equation}
S
=\begin{Bmatrix}
A & B & \cdots\ &C\\\\
D & E & \cdots\ & F
\end{Bmatrix}
\end{equation}

vmatrix

$$
\begin{equation}
S
=\begin{vmatrix}
A & B & \cdots\ &C\\
D & E & \cdots\ & F
\end{vmatrix}
\end{equation}
$$

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\begin{equation}
S
=\begin{vmatrix}
A & B & \cdots\ &C\\\\
D & E & \cdots\ & F
\end{vmatrix}
\end{equation}

Vmatrix

$$
\begin{equation}
S
=\begin{Vmatrix}
A & B & \cdots\ &C\\
D & E & \cdots\ & F
\end{Vmatrix}
\end{equation}
$$

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\begin{equation}
S
=\begin{Vmatrix}
A & B & \cdots\ &C\\\\
D & E & \cdots\ & F
\end{Vmatrix}
\end{equation}

Augmented Matrix

$$
\left[
\begin{array}{cc|c}
A & B & C \\
D & E & F
\end{array}
\right]
$$

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\left[
\begin{array}{cc|c}
A & B & C \\\\
D & E & F
\end{array}
\right]

Other Symbols

Symbol Syntax Symbol Syntax Symbol Syntax
$\infty$ \infty $\triangle$ \triangle $\angle$ \angle
$\checkmark$ \checkmark $\nabla$ \nabla
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Title:LaTeX数学符号速查表
Author:LIPENGZHA
Publish Date:2019/03/22 00:27
Update Date:2019/03/22 11:25
World Count:6.1k Words
Link:https://en.imzlp.com/posts/23224/
License: CC BY-NC-SA 4.0
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