LaTeX Mathematical Symbols Quick Lookup Table

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 ÷ \div

Power Operations

Symbol Syntax Symbol Syntax Symbol Syntax Symbol Syntax
ax a^x axyz a^{xyz} x \sqrt{x} xn \sqrt[n]{x}

Logical Operations

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

Absolute Value

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

|ivi|Δti||

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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.

(ax)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:

(ax)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 \int \oint \prod

Relations

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

Sets

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

Existence

Symbol Syntax Symbol Syntax
\exists \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 α \alpha β \beta γ \gamma
Uppercase Φ \Phi Ω \Omega Δ \Delta

Arrows

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

Ellipsis

Symbol Syntax Symbol Syntax
\dots \cdots

Accents

Symbol Syntax Symbol Syntax Symbol Syntax
x^ \hat{x} x¯ \bar{x} x \vec{x}
x˙ \dot{x} x¨ \ddot{x}

Standard Parentheses

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

Floor and Ceiling Functions

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

Spaces

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

Effect Description Syntax
ab 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 \
ab Space width is 36mu \qquad

Superscripts and Subscripts

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

Symbol Syntax Symbol Syntax
22 2^2 ai a_i
223 2^{23} ni1 n_{i-1}
a3i+1 a^{i+1}_3 x32 x^{3^2}
2ai 2^{a_i} 2ia 2^a_i

Overline and Underline

Over Syntax Under Syntax
a+bi \overline{a+bi} 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
12 \frac{1}{2} 12 \dfrac{1}{2}
2x+2 \frac{2}{x+2} 2x+2 \dfrac{2}{x+2}
1+1x3x+2 \frac{1+\frac{1}{x}}{3x + 2} 1+1x3x+2 \dfrac{1+\frac{1}{x}}{3x + 2}

Using consecutively (nested): \cfrac

Symbol Syntax
21+21+21+21 \cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}

Radical Expressions

Symbol Syntax Symbol Syntax
(2) \sqrt(2) 2 \sqrt{2}
x+y \sqrt{x+y} x+12 \sqrt{x+\frac{1}{2}}
33 \sqrt[3]{3} xn \sqrt[n]{x}

Summation, Product, Limit

Symbol Syntax
i=11i \sum_{i=1}^{\infty}\frac{1}{i}
n=15nn1 \prod_{n=1}^5\frac{n}{n-1}
limx1x \lim_{x\to\infty}\frac{1}{x}

Differentiation and Partial Derivatives

Symbol Syntax
ddx(x2)=2x \frac{d}{dx}\left(x^2\right) = 2x
2x,dx=x2+C \int 2x,dx = x^2+C
2Ux2+2Uy2 \frac{\partial^2U}{\partial x^2} + \frac{\partial^2U}{\partial y^2}

Modulus

93(mod6) —— 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
cos2x+sin2x=1 \cos^2 x +\sin^2 x = 1
cos90=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 &.

(1)Hx=13×[101101101],Hy=13×[111000111]

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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

(2)S=[AB CDE FGH I]

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\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 \cdots \ddots

matrix

AB CDE F

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

pmatrix

(3)S=(AB CDE F)

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

bmatrix

(4)S=[AB CDE F]

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

Bmatrix

(5)S={AB CDE F}

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

vmatrix

(6)S=|AB CDE F|

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

Vmatrix

(7)S=AB CDE F

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

Augmented Matrix

[ABCDEF]

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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 \triangle \angle
\checkmark \nabla
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Title:LaTeX Mathematical Symbols Quick Lookup Table
Author:LIPENGZHA
Publish Date:2019/03/22 00:27
Update Date:2019/03/22 11:25
Word Count:6.1k Words
Link:https://en.imzlp.com/posts/23224/
License: CC BY-NC-SA 4.0
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