LaTex Cheatsheet

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Special Characters / Symbols

No dot

\imath $\rightarrow$ $\imath$, \jmath $\rightarrow$ $\jmath$

Hat

\hat{\imath} $\rightarrow$ $\hat{\imath}$, \hat{\jmath} $\rightarrow$ $\hat{\jmath}$

Widehat \widehat{\beta} gives $\widehat{\beta}$

Ordinary hat \hat{\beta} gives $\hat{\beta}$.

Vectors

\vec: $\vec{A}$

\overrightarrow: $\overrightarrow{AB}$

Sample average: $\overline{X}$ (\overline{X}, line is longer), $\bar{X}$ (\bar{X}, bar is shorter)

\tilde{X}: $\tilde{X}$

\hat{\beta}: $\hat{\beta}$

Sometimes, hat or bar symbols look too light. You might want a bolder version of them.

\newcommand{\thickhat}[1]{\mathbf{\hat{\text{$#1$}}}}
\newcommand{\thickbar}[1]{\mathbf{\bar{\text{$#1$}}}}
\newcommand{\thicktilde}[1]{\mathbf{\tilde{\text{$#1$}}}}

Matrices

Type	LATEX markup	Renders as
Plain	\begin{matrix}1 & 2 & 3\\ a & b & c\end{matrix}	\(\begin{matrix}1 & 2 & 3\\ a & b & c\end{matrix}\)
Parentheses; round brackets	\begin{pmatrix}1 & 2 & 3\\ a & b & c\end{pmatrix}	\(\begin{pmatrix}1 & 2 & 3\\ a & b & c\end{pmatrix}\)
Brackets; square brackets	\begin{bmatrix}1 & 2 & 3\\ a & b & c\end{bmatrix}	\(\begin{bmatrix}1 & 2 & 3\\ a & b & c\end{bmatrix}\)
Braces; curly brackets	\begin{Bmatrix}1 & 2 & 3\\ a & b & c\end{Bmatrix}	\(\begin{Bmatrix}1 & 2 & 3\\ a & b & c\end{Bmatrix}\)
Pipes	\begin{vmatrix}1 & 2 & 3\\ a & b & c\end{vmatrix}	\(\begin{vmatrix}1 & 2 & 3\\ a & b & c\end{vmatrix}\)
Double pipes	\begin{Vmatrix}1 & 2 & 3\\ a & b & c\end{Vmatrix}	\(\begin{Vmatrix}1 & 2 & 3\\ a & b & c\end{Vmatrix}\)

Note:

• \\ for row break, & for column separation.
  • sometimes \\ doesn’t work in cloumn vectors, use \cr instead.

Common symbols	Matrices
$\boldsymbol{I}_n$ (\boldsymbol{I}_n)	$n\times n$ identity matrix
$\mathbb{1}_n$ (\mathbb{1} from \usepackage{bbold})	$n\times n$ identity matrix, double 1 representation
$\boldsymbol{1}_n$ (\boldsymbol{1}_n)	$n\times 1$ vector of ones
$\boldsymbol{1}(a)$ (\boldsymbol{1}(a))	Indicator function (1 if a is true, else 0)

Delimiters

Term	LaTeX	Symbol
Left angle	\langle	$\langle$
Right angle	\rangle	$\rangle$
Left bracket	\lbrack	$\lbrack$
Right bracket	\rbrack	$\rbrack$
Left brace	\lbrace	$\lbrace$
Right brace	\rbrace	$\rbrace$
Double vertical bar	\|	$|$

Greek Letters

Capital

LaTex		LaTex
\Gamma	Γ	\Delta	∆
\Lambda	Λ	\Phi	Φ
\Pi	Π	\Psi	Ψ
\Sigma	Σ	\Theta	Θ
\Upsilon	Υ	\Xi	Ξ
\Omega	Ω

Lowercase

LaTex		LaTex
\alpha	α	\nu	ν
\beta	β	\kappa	κ
\gamma	γ	\lambda	λ
\delta	δ	\mu	µ
\epsilon	ϵ	\zeta	ζ
\eta	η	\theta	θ
\iota	ι	\xi	ξ
\pi	π	\rho	ρ
\sigma	σ	\tau	τ
\upsilon	υ	\phi	φ
\chi	χ	\psi	ψ
\omega	ω

Other

LaTex		LaTex
\digamma	ϝ	varepsilon	ε
\varkappa	ϰ	\varphi	ϕ
\varpi	$\varpi$	\varrho	ϱ
\varsigma	$\varsigma$	\vartheta	ϑ
\eth	ð	\hbar	$\hbar$

Other Symbols

LaTex		LaTex
\partial	∂	\infty	∞
\wedge	∧	\vee	∨
\neg \not	¬
\bot	⊥	\top	⊤
\nabla	∇	\varnothing	∅
\angle	∠	\measuredangle	∡
\surd	√	\forall	∀
\lceil{x}\rceil	$\left \lceil{x}\right \rceil $	\lfloor x \rfloor	$\lfloor x \rfloor$

• ' prime symbol is a shorthand for ^\prime .

QED

When creating TeX, Knuth provided the symbol $\blacksquare$ (black square, \blacksquare), also called by mathematicians tombstone or Halmos symbol (after Paul Halmos, who pioneered its use).

The tombstone is sometimes open: $\square$ (white square, \square) or $\Box$ (\Box).

HTML and XML provide ways to reference Unicode characters when the characters themselves either cannot or should not be used.

Unicode characters for geometric shapes: http://www.unicode.org/charts/nameslist/n_25A0.html

A numeric character reference uses the format&#nnnn; or &#xhhhh;. nnnn is in decimal form, hhhh is in hexadecimal form. The &# and ; are required.

Sets

LaTex		LaTex
\cap	$\cap$	\cup	$\cup$
\subset	$\subset$	\subseteq	$\subseteq$
\supset	$\supset$	\supseteq	$\supseteq$
\subsetneq	$\subsetneq$	\supsetneq	$\supsetneq$
\in	$\in$	\notin	$\notin$
\exists	$\exists$	\not\exists	$\not\exists$
\forall	$\forall$	\emptyset or \varnothing	$\emptyset$, $\varnothing$

• use \not before an operator to negate it.

Binary operators

LaTex		LaTex
\wedge	∧ (and)	\vee	∨ (or)
\neg	$\neg$ (not)	\div	$\div$
\ast	$\ast$	\times	$\times$

Relational Symbols

LaTex		LaTex
\geq	≥	\leq	≤
\equiv	≡	\sim	$\sim$
\gg	≫	\ll	$\ll$
\mid	$\mid$	\propto	$\propto$
\perp	⊥	\parallel	$\parallel$
\vartriangle	$\vartriangle$	\leadsto	$\leadsto$
\triangleq	$\triangleq$	\approx	$\approx$
\triangledown	$\triangledown$	\nabla	$\nabla$

Note:

• use \vert or \mid ($\vert$) to show a pipe operator, otherwise Markdown recognizes it as a table column separator in inline equations (block equations enclosed in $$...$$ works fine though).

  • \lVert and \rVert ($\rVert$) used to take the norm of a vector;

  • \lvert and \vert ($\lvert$) used to take absolute value of real numbers and modulus of complex numbers;

  • \mid is often used as delimitor, ${a\in S \mid \text{(a=0) or (a) is odd}}$; $\mid$ in set theory means “such that”, to introduce properties of the set; in probability, meaning conditional on;

  • \mid is also used to divide numbers. $4 \mid 12=3$, meaning $\text{(4) divides (12)}$. $a \mid b$ meaning $b$ is completely divisible by $a$. E.g., \(\{𝑥\in \mathbb{Z}\mid 4\mid𝑥\}\)

    which describes the set of integers which 4 divides, namely ${0,\pm4,\pm8,\pm12,…}$. Some people prefer to use a colon there

    \[\{𝑥\in \mathbb{Z}: 4\mid 𝑥 \}.\]

  • \mid can be used in conditional probabilities. \(p\text{-value} = P(Z\le z \mid H_0 \text{ is true}) = F(z)\) \mid creates nicer margins to the left and right compared to \vert.

• \perp ($\perp$) indicates zero correlation; \indep ($\indep$) indicates independece.

• $\triangleq$ and := used to define a variable using the RHS.

  $\equiv$ (\equiv) is used to denote shorthand. There is no logical or physical content here; two expressions which are separated by $\equiv$ have exactly the same meaning, but are written a different way.

• $\vartriangle$ is a math operator, standing for increment, should be up right;

  • $\Delta$ is a Greek letter, should be italic

• $\nabla$ commonly used to denote increments.

  \[\nabla_1 h(x_1, \boldsymbol{x_2}, \boldsymbol{u}) = h(1,\boldsymbol{x_2}, \boldsymbol{u})-h(0,\boldsymbol{x_2}, \boldsymbol{u}) .\]

• $\sim$ means

  • “sampled from” or “has the distribution of”,

  • “of the order of”, “approximately equal to”,

  • “proportional to”.

• $\propto$ (\propto) means proportional to.

• $\overset{\text{aprrox}}{\sim}$ (\overset{\text{aprrox}}{\sim}) for approximately distributed with.

  $\;\;\overset{\text{a}}{\sim}\;\;$ (\overset{\text{a}}{\sim}) indicates that the distributional relation is asymptotic.

  $\;\;\overset{\text{a}}{=}\;\;$ (\overset{\text{a}}{=}) indicates that the equality holds asymptotically.

Arrows

LaTex	Symbol	LaTex	Symbol
\hookrightarrow	↪	\rightarrow	$\rightarrow$
\Rightarrow	$\Rightarrow$	\Leftrightarrow	$\Leftrightarrow$
\implies	$\implies$	\iff	$\iff$
\nrightarrow	↛	\mapsto	$\mapsto$
\nearrow	$\nearrow$	\searrow	$\searrow$
\uparrow	$\uparrow$	\downarrow	$\downarrow$

• $\rightarrow$ denotes a mapping between two sets. 两边都是集合。

  $\mapsto$ called mapsto, tells you what it does to each element of the set. 两边是数值的一个transform。

  For example, I can define a function $𝑓:\mathbb{R}\rightarrow\mathbb{R}$ by $𝑓(𝑥):=2𝑥$. Notice that the $\rightarrow$ is between the two real number sets. But, I can also express that $𝑓(3)=6$ by $3\mapsto 6$. More generally, $𝑓(𝑥):=2𝑥$ can be written as $𝑥 \mapsto 2𝑥$.

• Text above or under symbols or other text, e.g., $\sim$

  • \overset{#1}{#2} put argument #1 (in script style) over argument #2. E.g., $\overset{\text{a}}{\sim}$ \overset{\text{a}}{\sim} or \overset{\rm a}{\sim}. \rm for Roman font (upright). A side note: Words in subscripts or superscripts should be upright.

  • \underset{#1}{#2} put argument #1 (in script style) under argument #2. E.g., \(\begin{align*} \widetilde{\beta}_{k}^{\rm ridge} &= \underset{b\in \mathbb{R}^{p+1}}{\rm arg\, min} \lVert y-X b \rVert ^{2} \\ \hat{\boldsymbol{\beta}} &= \arg\underset{\boldsymbol{\beta}}{\min} \sum_{i=1}^n \varepsilon_i^2 \end{align*}\) \arg\underset{\boldsymbol{\beta}}{\min} gives you $\arg\underset{\boldsymbol{\beta}}{\min}$.

• Text above arrows. $\xrightarrow{d}$ \xrightarrow{d} convergence in distribution.

Cumulative operators

LaTex		LaTex
\int	∫	\iint	$\iint$
\iiint	$\iiint$	\idotsint	$\idotsint$
\prod	$\prod$	\sum	$\sum$
\bigcup	$\bigcup$	\bigcap	$\bigcap$

Summation operators: $\displaystyle\sum_{i=1}^n$ (\displaystyle\sum_{i=1}^n) vs $\textstyle\sum_{i=1}^n$ (\textstyle\sum_{i=1}^n).

• \displaystyle apply the style used for mathematics typeset on lines by themselves.
• \textstyle apply the style used for mathematics typeset in paragraphs.

\lim_{n\to\infty} for inline limits: $\lim_{n\to\infty}$

\displaystyle\lim_{n\to\infty} for display limits: $\displaystyle\lim_{n\to\infty}$

$X_n \xrightarrow{p} c$ convergence in probability: $X_n \xrightarrow{p} c$

Differtials

Display shows eqns in block, text style shows inline.

• \dfrac used to show display style. $\dfrac{\partial f}{\partial x}$

• \tfrac used to show text style. $\tfrac{\partial f}{\partial x}$

In terms of ordinary derivative, d should be upright as it is not a variable.

Use derivative package to format differtials.

\usepackage{derivative}


\begin{align*}
& \quad &\text{partial derivative: }  & \pdv{f}{x} \\
&  &\text{partial derivative: }  & \pdv{f}{x,y} \\
&  &\text{partial derivative with star (*): }  & \pdv*{f}{x,y} \\
& & \text{higher order derivative: } & \odv*{\odv[delims-frac=(), frac
]{y}{x}}{x} \\
& & \text{ordinary derivative: } & \odv{s}{t} \\
& & \text{higher order derivative: } & \odv[switch-*=false, order=n]{y}{x} \\
\end{align*}

Ellipsis

• \ldots are used between commas, e.g., $a_1, \ldots, a_n$ ;

  \cdots used between plus/minus signs, e.g., $a_1+ \cdots + a_n$ ;

  \ddots often used in matrices, e.g., \(\boldsymbol{X} = \begin{pmatrix} x_1'\\ x_2'\\ \vdots \\ x_n'\\ \end{pmatrix} = \begin{pmatrix} x_{11} & x_{21} & \cdots & x_{K1} \\ x_{12} & x_{22} & \cdots & x_{K2} \\ \vdots & \vdots & \ddots & \vdots \\ x_{1n} & x_{2n} & \cdots & x_{Kn} \end{pmatrix}_{n\times K}\)

Interpunct

An interpunct ⟨·⟩, also known as an interpoint, middle dot, middot, centered dot or centred dot, is a punctuation mark consisting of a vertically centered dot used for interword separation in Classical Latin.

On mac, use Shift+Opt+9 to type ·

Named operators

$\arccos$, $\arcsin$, $\arctan$, $\cos$, $\cosh$, $\cot$, $\coth$, $\sec$, $\sin$, $\sinh$,

$\deg$, $\det$, $\dim$, ${\color{#32CD32}\exp}$, $\gcd$, $\hom$, $\injlim$, $\projlim$,

$\lim$, $\liminf$, $\limsup$,

$\ln$ (natural logarithm), $\log$, $\lg$ (the logarithm to base 10),

$\max$, $\min$, $\arg$, $\Pr$,

$\sup$, $\inf$

Note:

• \right . creates an “invisible” delimiter that is used to match a corresponding \left, e.g., in multi-case function definition, you only need one left brace, then you use \right . to indicate the end of the function.

• In markdown, you can define your own commands by putting the following codes at the beginning of the file.

  $$
  \newcommand{\indep}{\perp \!\!\! \perp}
  $$
  

• Curly braces in eqns need to be escaped. \{ ... \} or \\{ ... \\} (the slash needs to be escaped itself). E.g.,

  • $\exp \{ \ldots \}$ (\exp \\{ \ldots \\})

  • $\exp \{-\frac{1}{2}\left(\frac{x-\mu}{\sigma^2}\right)^2 \}$ (\exp \\{-\frac{1}{2}\left(\frac{x-\mu}{\sigma^2}\right)^2 \\})

  • If still encounter problems, use \lbrace and \rbrace: $\exp \lbrace \ldots \rbrace$ (\exp \lbrace \ldots \rbrace) and $\lbrace Z_t \rbrace_{t=0}^T$ (\lbrace Z_t \rbrace_{t=0}^T). This is the safest way.

  • Use \left\lbrace and \right\rbrace if you want to scale the braces with the expression inside. This is called “dynamic delimiter sizing.”

    You could also use \left\{ and \right\}.

    Here is a nice guide.

• Square brakets: $E\lbrack x \rbrack$ (E\lbrack x \rbrack)

• Add whitespace between equations, use \quad, \qquad, and \hspace{20pt} for long space; and \; for short space.

• $\min_{\forall s \in S_j} q_k(s)$ (\min_{\forall s \in S_j} q_k(s)) text under min/max.

Colored math symbols

${\color{#32CD32}\exp}$ ${\color{#32CD32}\exp}$ Need to quote the part you want to color in curly braces; otherwise, everything behind will change color too.

Escaped/Reserved Characters

The reserved characters have, in addition to the pure representation of the character, an additional function. Therefore, they cannot be used simply because it is generally assumed first that the function and not the character is meant.

https://www.sascha-frank.com/reserved_characters.html

\	masks special characters and initiates commands.
{ }	Contains arguments, creates text blocks
%	Comment character: The rest of the line is ignored.
^	Exponent in math mode
_	Index in math mode
&	depending on context - Tabulator
#	Parameters
~	Protected space.
[,]	Square brackets
<,>	Lace braces
”	Quotation marks

Reference

@LKS90, Github Repository, https://gist.github.com/LKS90/252ac41bd4a173be35b0.