LaTeX Mathematical Symbols Quick Lookup Table

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.

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

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 &.

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

\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

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

\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

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

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

pmatrix

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

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

bmatrix

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

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

Bmatrix

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

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

vmatrix

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

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

Vmatrix

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

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

Augmented Matrix

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

\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