48 LaTeX Command Reference

This appendix provides a comprehensive reference for LaTeX mathematical notation commands commonly used in Quarto and R Markdown documents.

48.1 Greek Letters

Lowercase Greek Letters

Symbol	Command	Symbol	Command	Symbol	Command
$\alpha$	`\alpha`	$\iota$	`\iota`	$\rho$	`\rho`
$\beta$	`\beta`	$\kappa$	`\kappa`	$\sigma$	`\sigma`
$\gamma$	`\gamma`	$\lambda$	`\lambda`	$\tau$	`\tau`
$\delta$	`\delta`	$\mu$	`\mu`	$\upsilon$	`\upsilon`
$\epsilon$	`\epsilon`	$\nu$	`\nu`	$\phi$	`\phi`
$\varepsilon$	`\varepsilon`	$\xi$	`\xi`	$\varphi$	`\varphi`
$\zeta$	`\zeta`	$\pi$	`\pi`	$\chi$	`\chi`
$\eta$	`\eta`	$\varpi$	`\varpi`	$\psi$	`\psi`
$\theta$	`\theta`	$\omega$	`\omega`	$\varsigma$	`\varsigma`
$\vartheta$	`\vartheta`

Uppercase Greek Letters

Symbol	Command	Symbol	Command	Symbol	Command
$\Gamma$	`\Gamma`	$\Xi$	`\Xi`	$\Phi$	`\Phi`
$\Delta$	`\Delta`	$\Pi$	`\Pi`	$\Psi$	`\Psi`
$\Theta$	`\Theta`	$\Sigma$	`\Sigma`	$\Omega$	`\Omega`
$\Lambda$	`\Lambda`	$\Upsilon$	`\Upsilon`

48.2 Arithmetic Operations

Symbol	Command	Description	Example
$+$	`+`	Addition	$a + b$
$-$	`-`	Subtraction	$a - b$
$\times$	`\times`	Multiplication	$a \times b$
$\cdot$	`\cdot`	Centered dot	$a \cdot b$
$\div$	`\div`	Division	$a \div b$
$\frac{a}{b}$	`\frac{a}{b}`	Fraction	$\frac{x}{y}$
$\pm$	`\pm`	Plus or minus	$\pm 5$
$\mp$	`\mp`	Minus or plus	$\mp 5$

48.3 Powers and Indices

Symbol	Command	Description	Example
$x^n$	`x^n`	Superscript	$x^2$
$x_n$	`x_n`	Subscript	$x_1$
$x^{n+1}$	`x^{n+1}`	Multi-char superscript	$x^{ab}$
$x_{i,j}$	`x_{i,j}`	Multi-char subscript	$x_{ij}$
$x_n^2$	`x_n^2`	Combined	$x_i^2$
$\sqrt{x}$	`\sqrt{x}`	Square root	$\sqrt{16}$
$\sqrt[n]{x}$	`\sqrt[n]{x}`	nth root	$\sqrt[3]{8}$

48.4 Relation Operators

Symbol	Command	Description
$=$	`=`	Equal to
$\neq$	`\neq`	Not equal to
$<$	`<`	Less than
$>$	`>`	Greater than
$\leq$	`\leq`	Less than or equal
$\geq$	`\geq`	Greater than or equal
$\ll$	`\ll`	Much less than
$\gg$	`\gg`	Much greater than
$\approx$	`\approx`	Approximately equal
$\sim$	`\sim`	Similar to / distributed as
$\simeq$	`\simeq`	Similar or equal
$\cong$	`\cong`	Congruent
$\equiv$	`\equiv`	Equivalent
$\propto$	`\propto`	Proportional to
$\doteq$	`\doteq`	Approaches the limit

48.5 Set Theory

Symbol	Command	Description
$\in$	`\in`	Element of
$\notin$	`\notin`	Not element of
$\ni$	`\ni`	Contains as element
$\subset$	`\subset`	Proper subset
$\subseteq$	`\subseteq`	Subset or equal
$\supset$	`\supset`	Proper superset
$\supseteq$	`\supseteq`	Superset or equal
$\cap$	`\cap`	Intersection
$\cup$	`\cup`	Union
$\setminus$	`\setminus`	Set difference
$\emptyset$	`\emptyset`	Empty set
$\varnothing$	`\varnothing`	Empty set (variant)

48.6 Logic Symbols

Symbol	Command	Description
$\land$	`\land`	Logical AND
$\lor$	`\lor`	Logical OR
$\neg$	`\neg`	Logical NOT
$\forall$	`\forall`	For all
$\exists$	`\exists`	There exists
$\nexists$	`\nexists`	There does not exist
$\Rightarrow$	`\Rightarrow`	Implies
$\Leftarrow$	`\Leftarrow`	Is implied by
$\Leftrightarrow$	`\Leftrightarrow`	If and only if
$\therefore$	`\therefore`	Therefore
$\because$	`\because`	Because

48.7 Arrows

Symbol	Command	Symbol	Command
$\rightarrow$	`\rightarrow`	$\leftarrow$	`\leftarrow`
$\Rightarrow$	`\Rightarrow`	$\Leftarrow$	`\Leftarrow`
$\leftrightarrow$	`\leftrightarrow`	$\Leftrightarrow$	`\Leftrightarrow`
$\longrightarrow$	`\longrightarrow`	$\longleftarrow$	`\longleftarrow`
$\uparrow$	`\uparrow`	$\downarrow$	`\downarrow`
$\Uparrow$	`\Uparrow`	$\Downarrow$	`\Downarrow`
$\nearrow$	`\nearrow`	$\searrow$	`\searrow`
$\nwarrow$	`\nwarrow`	$\swarrow$	`\swarrow`
$\mapsto$	`\mapsto`	$\to$	`\to`

48.8 Sums, Products, and Integrals

Symbol	Command	Example
$\sum$	`\sum`	$\sum_{i=1}^{n} x_i$
$\prod$	`\prod`	$\prod_{i=1}^{n} x_i$
$\coprod$	`\coprod`	$\coprod_{i=1}^{n}$
$\int$	`\int`	$\int_a^b f(x) dx$
$\iint$	`\iint`	$\iint_D f(x,y) dA$
$\iiint$	`\iiint`	$\iiint_V f dV$
$\oint$	`\oint`	$\oint_C F \cdot dr$
$\bigcup$	`\bigcup`	$\bigcup_{i=1}^{n} A_i$
$\bigcap$	`\bigcap`	$\bigcap_{i=1}^{n} A_i$
$\bigoplus$	`\bigoplus`	$\bigoplus_{i=1}^{n}$
$\bigotimes$	`\bigotimes`	$\bigotimes_{i=1}^{n}$
$\lim$	`\lim`	$\lim_{x \to 0}$
$\limsup$	`\limsup`	$\limsup_{n \to \infty}$
$\liminf$	`\liminf`	$\liminf_{n \to \infty}$

48.9 Mathematical Functions

Symbol	Command	Symbol	Command
$\sin$	`\sin`	$\arcsin$	`\arcsin`
$\cos$	`\cos`	$\arccos$	`\arccos`
$\tan$	`\tan`	$\arctan$	`\arctan`
$\cot$	`\cot`	$\sec$	`\sec`
$\csc$	`\csc`	$\sinh$	`\sinh`
$\cosh$	`\cosh`	$\tanh$	`\tanh`
$\log$	`\log`	$\ln$	`\ln`
$\lg$	`\lg`	$\exp$	`\exp`
$\max$	`\max`	$\min$	`\min`
$\sup$	`\sup`	$\inf$	`\inf`
$\arg$	`\arg`	$\det$	`\det`
$\dim$	`\dim`	$\ker$	`\ker`
$\gcd$	`\gcd`	$\deg$	`\deg`
$\hom$	`\hom`	$\Pr$	`\Pr`

48.10 Accents and Decorations

Symbol	Command	Description
$\hat{x}$	`\hat{x}`	Hat (estimator)
$\widehat{xyz}$	`\widehat{xyz}`	Wide hat
$\bar{x}$	`\bar{x}`	Bar (mean)
$\overline{xyz}$	`\overline{xyz}`	Overline
$\tilde{x}$	`\tilde{x}`	Tilde
$\widetilde{xyz}$	`\widetilde{xyz}`	Wide tilde
$\vec{x}$	`\vec{x}`	Vector arrow
$\overrightarrow{AB}$	`\overrightarrow{AB}`	Vector from A to B
$\dot{x}$	`\dot{x}`	Dot (time derivative)
$\ddot{x}$	`\ddot{x}`	Double dot
$\acute{x}$	`\acute{x}`	Acute accent
$\grave{x}$	`\grave{x}`	Grave accent
$\breve{x}$	`\breve{x}`	Breve
$\check{x}$	`\check{x}`	Check mark

48.11 Font Styles

Symbol	Command	Description
$\mathbf{x}$	`\mathbf{x}`	Bold (vectors/matrices)
$\mathit{x}$	`\mathit{x}`	Italic
$\mathrm{x}$	`\mathrm{x}`	Roman (upright)
$\mathsf{x}$	`\mathsf{x}`	Sans-serif
$\mathtt{x}$	`\mathtt{x}`	Typewriter
$\mathcal{X}$	`\mathcal{X}`	Calligraphic
$\mathbb{R}$	`\mathbb{R}`	Blackboard bold
$\mathfrak{X}$	`\mathfrak{X}`	Fraktur
$\boldsymbol{\alpha}$	`\boldsymbol{\alpha}`	Bold symbol (Greek)

48.12 Common Number Sets

Symbol	Command	Description
$\mathbb{N}$	`\mathbb{N}`	Natural numbers
$\mathbb{Z}$	`\mathbb{Z}`	Integers
$\mathbb{Q}$	`\mathbb{Q}`	Rational numbers
$\mathbb{R}$	`\mathbb{R}`	Real numbers
$\mathbb{C}$	`\mathbb{C}`	Complex numbers
$\mathbb{P}$	`\mathbb{P}`	Prime numbers

48.13 Brackets and Delimiters

Symbol	Command	Description
$(x)$	`(x)`	Parentheses
$[x]$	`[x]`	Square brackets
$\{x\}$	`\{x\}`	Curly braces
$\langle x \rangle$	`\langle x \rangle`	Angle brackets
$\|x\|$	`\|x\|`	Vertical bars (absolute value)
$\\|x\\|$	`\\|x\\|`	Double bars (norm)
$\lfloor x \rfloor$	`\lfloor x \rfloor`	Floor
$\lceil x \rceil$	`\lceil x \rceil`	Ceiling

Auto-sizing Delimiters

Use \left and \right for automatically sized delimiters:

Example	Code
$\left( \frac{a}{b} \right)$	`\left( \frac{a}{b} \right)`
$\left[ \sum_{i=1}^{n} x_i \right]$	`\left[ \sum_{i=1}^{n} x_i \right]`
$\left\{ \frac{a}{b} \right\}$	`\left\{ \frac{a}{b} \right\}`
$\left\| \frac{a}{b} \right\|$	`\left\| \frac{a}{b} \right\|`

48.14 Matrix Environments

Environment	Result	Brackets
`matrix`	$\begin{matrix} a & b \\ c & d \end{matrix}$	None
`pmatrix`	$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$	Parentheses
`bmatrix`	$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$	Square brackets
`Bmatrix`	$\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}$	Curly braces
`vmatrix`	$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$	Vertical bars
`Vmatrix`	$\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}$	Double vertical

Syntax:

$$\begin{bmatrix}
a & b & c \\
d & e & f
\end{bmatrix}$$

48.15 Spacing

Command	Width	Example
`\,`	3/18 em (thin)	$a\,b$
`\:`	4/18 em (medium)	$a\:b$
`\;`	5/18 em (thick)	$a\;b$
`\quad`	1 em	$a\quad b$
`\qquad`	2 em	$a\qquad b$
`\!`	-3/18 em (negative)	$a\!b$

48.16 Dots and Ellipses

Symbol	Command	Usage
$\ldots$	`\ldots`	Baseline dots
$\cdots$	`\cdots`	Centered dots
$\vdots$	`\vdots`	Vertical dots
$\ddots$	`\ddots`	Diagonal dots
$\cdot$	`\cdot`	Single centered dot

48.17 Miscellaneous Symbols

Symbol	Command	Description
$\infty$	`\infty`	Infinity
$\partial$	`\partial`	Partial derivative
$\nabla$	`\nabla`	Nabla / Del
$\prime$	`\prime`	Prime
$\angle$	`\angle`	Angle
$\triangle$	`\triangle`	Triangle
$\square$	`\square`	Square
$\circ$	`\circ`	Circle / composition
$\bullet$	`\bullet`	Bullet
$\star$	`\star`	Star
$\dagger$	`\dagger`	Dagger
$\ddagger$	`\ddagger`	Double dagger
$\ell$	`\ell`	Script l
$\hbar$	`\hbar`	h-bar (Planck’s constant)
$\Re$	`\Re`	Real part
$\Im$	`\Im`	Imaginary part
$\aleph$	`\aleph`	Aleph

48.18 Statistical Notation

Expression	Code	Description
$\bar{x}$	`\bar{x}`	Sample mean
$\hat{\mu}$	`\hat{\mu}`	Estimated parameter
$\tilde{x}$	`\tilde{x}`	Median
$X \sim N(\mu, \sigma^2)$	`X \sim N(\mu, \sigma^2)`	Distribution
${n \choose k}$	`{n \choose k}`	Binomial coefficient
$\binom{n}{k}$	`\binom{n}{k}`	Binomial coefficient (alternate)
$P(A \mid B)$	`P(A \mid B)`	Conditional probability
$\mathbb{E}[X]$	`\mathbb{E}[X]`	Expected value
$\text{Var}(X)$	`\text{Var}(X)`	Variance
$\text{Cov}(X, Y)$	`\text{Cov}(X, Y)`	Covariance

48.19 Common Statistical Formulas

Sample Statistics

Statistic	Formula
Sample mean	$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$
Sample variance	$s^2 = \frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2$
Standard error	$SE = \frac{s}{\sqrt{n}}$
Z-score	$z = \frac{x - \mu}{\sigma}$

Probability Distributions

Distribution	Probability Function
Binomial	$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$
Poisson	$P(X=k) = \frac{e^{-\lambda}\lambda^k}{k!}$
Normal	$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$
Exponential	$f(x) = \lambda e^{-\lambda x}$

48.20 Equation Numbering in Quarto

Add equation labels for cross-referencing:

$$
E = mc^2
$$ {#eq-einstein}

See @eq-einstein for the mass-energy equivalence.

Multiple equations with alignment:

$$
\begin{aligned}
y &= mx + b \\
  &= 2x + 3
\end{aligned}
$$ {#eq-line}

# LaTeX Command Reference {#sec-appendix-latex} This appendix provides a comprehensive reference for LaTeX mathematical notation commands commonly used in Quarto and R Markdown documents. ## Greek Letters {#sec-latex-greek} ### Lowercase Greek Letters {#sec-latex-greek-lower} | Symbol | Command | Symbol | Command | Symbol | Command | |:------:|:--------|:------:|:--------|:------:|:--------| | $\alpha$ | `\alpha` | $\iota$ | `\iota` | $\rho$ | `\rho` | | $\beta$ | `\beta` | $\kappa$ | `\kappa` | $\sigma$ | `\sigma` | | $\gamma$ | `\gamma` | $\lambda$ | `\lambda` | $\tau$ | `\tau` | | $\delta$ | `\delta` | $\mu$ | `\mu` | $\upsilon$ | `\upsilon` | | $\epsilon$ | `\epsilon` | $\nu$ | `\nu` | $\phi$ | `\phi` | | $\varepsilon$ | `\varepsilon` | $\xi$ | `\xi` | $\varphi$ | `\varphi` | | $\zeta$ | `\zeta` | $\pi$ | `\pi` | $\chi$ | `\chi` | | $\eta$ | `\eta` | $\varpi$ | `\varpi` | $\psi$ | `\psi` | | $\theta$ | `\theta` | $\omega$ | `\omega` | $\varsigma$ | `\varsigma` | | $\vartheta$ | `\vartheta` | | | | | ### Uppercase Greek Letters {#sec-latex-greek-upper} | Symbol | Command | Symbol | Command | Symbol | Command | |:------:|:--------|:------:|:--------|:------:|:--------| | $\Gamma$ | `\Gamma` | $\Xi$ | `\Xi` | $\Phi$ | `\Phi` | | $\Delta$ | `\Delta` | $\Pi$ | `\Pi` | $\Psi$ | `\Psi` | | $\Theta$ | `\Theta` | $\Sigma$ | `\Sigma` | $\Omega$ | `\Omega` | | $\Lambda$ | `\Lambda` | $\Upsilon$ | `\Upsilon` | | | ## Arithmetic Operations {#sec-latex-arithmetic} | Symbol | Command | Description | Example | |:------:|:--------|:------------|:--------| | $+$ | `+` | Addition | `$a + b$` | | $-$ | `-` | Subtraction | `$a - b$` | | $\times$ | `\times` | Multiplication | `$a \times b$` | | $\cdot$ | `\cdot` | Centered dot | `$a \cdot b$` | | $\div$ | `\div` | Division | `$a \div b$` | | $\frac{a}{b}$ | `\frac{a}{b}` | Fraction | `$\frac{x}{y}$` | | $\pm$ | `\pm` | Plus or minus | `$\pm 5$` | | $\mp$ | `\mp` | Minus or plus | `$\mp 5$` | ## Powers and Indices {#sec-latex-powers} | Symbol | Command | Description | Example | |:------:|:--------|:------------|:--------| | $x^n$ | `x^n` | Superscript | `$x^2$` | | $x_n$ | `x_n` | Subscript | `$x_1$` | | $x^{n+1}$ | `x^{n+1}` | Multi-char superscript | `$x^{ab}$` | | $x_{i,j}$ | `x_{i,j}` | Multi-char subscript | `$x_{ij}$` | | $x_n^2$ | `x_n^2` | Combined | `$x_i^2$` | | $\sqrt{x}$ | `\sqrt{x}` | Square root | `$\sqrt{16}$` | | $\sqrt[n]{x}$ | `\sqrt[n]{x}` | nth root | `$\sqrt[3]{8}$` | ## Relation Operators {#sec-latex-relations} | Symbol | Command | Description | |:------:|:--------|:------------| | $=$ | `=` | Equal to | | $\neq$ | `\neq` | Not equal to | | $<$ | `<` | Less than | | $>$ | `>` | Greater than | | $\leq$ | `\leq` | Less than or equal | | $\geq$ | `\geq` | Greater than or equal | | $\ll$ | `\ll` | Much less than | | $\gg$ | `\gg` | Much greater than | | $\approx$ | `\approx` | Approximately equal | | $\sim$ | `\sim` | Similar to / distributed as | | $\simeq$ | `\simeq` | Similar or equal | | $\cong$ | `\cong` | Congruent | | $\equiv$ | `\equiv` | Equivalent | | $\propto$ | `\propto` | Proportional to | | $\doteq$ | `\doteq` | Approaches the limit | ## Set Theory {#sec-latex-sets} | Symbol | Command | Description | |:------:|:--------|:------------| | $\in$ | `\in` | Element of | | $\notin$ | `\notin` | Not element of | | $\ni$ | `\ni` | Contains as element | | $\subset$ | `\subset` | Proper subset | | $\subseteq$ | `\subseteq` | Subset or equal | | $\supset$ | `\supset` | Proper superset | | $\supseteq$ | `\supseteq` | Superset or equal | | $\cap$ | `\cap` | Intersection | | $\cup$ | `\cup` | Union | | $\setminus$ | `\setminus` | Set difference | | $\emptyset$ | `\emptyset` | Empty set | | $\varnothing$ | `\varnothing` | Empty set (variant) | ## Logic Symbols {#sec-latex-logic} | Symbol | Command | Description | |:------:|:--------|:------------| | $\land$ | `\land` | Logical AND | | $\lor$ | `\lor` | Logical OR | | $\neg$ | `\neg` | Logical NOT | | $\forall$ | `\forall` | For all | | $\exists$ | `\exists` | There exists | | $\nexists$ | `\nexists` | There does not exist | | $\Rightarrow$ | `\Rightarrow` | Implies | | $\Leftarrow$ | `\Leftarrow` | Is implied by | | $\Leftrightarrow$ | `\Leftrightarrow` | If and only if | | $\therefore$ | `\therefore` | Therefore | | $\because$ | `\because` | Because | ## Arrows {#sec-latex-arrows} | Symbol | Command | Symbol | Command | |:------:|:--------|:------:|:--------| | $\rightarrow$ | `\rightarrow` | $\leftarrow$ | `\leftarrow` | | $\Rightarrow$ | `\Rightarrow` | $\Leftarrow$ | `\Leftarrow` | | $\leftrightarrow$ | `\leftrightarrow` | $\Leftrightarrow$ | `\Leftrightarrow` | | $\longrightarrow$ | `\longrightarrow` | $\longleftarrow$ | `\longleftarrow` | | $\uparrow$ | `\uparrow` | $\downarrow$ | `\downarrow` | | $\Uparrow$ | `\Uparrow` | $\Downarrow$ | `\Downarrow` | | $\nearrow$ | `\nearrow` | $\searrow$ | `\searrow` | | $\nwarrow$ | `\nwarrow` | $\swarrow$ | `\swarrow` | | $\mapsto$ | `\mapsto` | $\to$ | `\to` | ## Sums, Products, and Integrals {#sec-latex-big-operators} | Symbol | Command | Example | |:------:|:--------|:--------| | $\sum$ | `\sum` | `$\sum_{i=1}^{n} x_i$` | | $\prod$ | `\prod` | `$\prod_{i=1}^{n} x_i$` | | $\coprod$ | `\coprod` | `$\coprod_{i=1}^{n}$` | | $\int$ | `\int` | `$\int_a^b f(x) dx$` | | $\iint$ | `\iint` | `$\iint_D f(x,y) dA$` | | $\iiint$ | `\iiint` | `$\iiint_V f dV$` | | $\oint$ | `\oint` | `$\oint_C F \cdot dr$` | | $\bigcup$ | `\bigcup` | `$\bigcup_{i=1}^{n} A_i$` | | $\bigcap$ | `\bigcap` | `$\bigcap_{i=1}^{n} A_i$` | | $\bigoplus$ | `\bigoplus` | `$\bigoplus_{i=1}^{n}$` | | $\bigotimes$ | `\bigotimes` | `$\bigotimes_{i=1}^{n}$` | | $\lim$ | `\lim` | `$\lim_{x \to 0}$` | | $\limsup$ | `\limsup` | `$\limsup_{n \to \infty}$` | | $\liminf$ | `\liminf` | `$\liminf_{n \to \infty}$` | ## Mathematical Functions {#sec-latex-functions} | Symbol | Command | Symbol | Command | |:------:|:--------|:------:|:--------| | $\sin$ | `\sin` | $\arcsin$ | `\arcsin` | | $\cos$ | `\cos` | $\arccos$ | `\arccos` | | $\tan$ | `\tan` | $\arctan$ | `\arctan` | | $\cot$ | `\cot` | $\sec$ | `\sec` | | $\csc$ | `\csc` | $\sinh$ | `\sinh` | | $\cosh$ | `\cosh` | $\tanh$ | `\tanh` | | $\log$ | `\log` | $\ln$ | `\ln` | | $\lg$ | `\lg` | $\exp$ | `\exp` | | $\max$ | `\max` | $\min$ | `\min` | | $\sup$ | `\sup` | $\inf$ | `\inf` | | $\arg$ | `\arg` | $\det$ | `\det` | | $\dim$ | `\dim` | $\ker$ | `\ker` | | $\gcd$ | `\gcd` | $\deg$ | `\deg` | | $\hom$ | `\hom` | $\Pr$ | `\Pr` | ## Accents and Decorations {#sec-latex-accents} | Symbol | Command | Description | |:------:|:--------|:------------| | $\hat{x}$ | `\hat{x}` | Hat (estimator) | | $\widehat{xyz}$ | `\widehat{xyz}` | Wide hat | | $\bar{x}$ | `\bar{x}` | Bar (mean) | | $\overline{xyz}$ | `\overline{xyz}` | Overline | | $\tilde{x}$ | `\tilde{x}` | Tilde | | $\widetilde{xyz}$ | `\widetilde{xyz}` | Wide tilde | | $\vec{x}$ | `\vec{x}` | Vector arrow | | $\overrightarrow{AB}$ | `\overrightarrow{AB}` | Vector from A to B | | $\dot{x}$ | `\dot{x}` | Dot (time derivative) | | $\ddot{x}$ | `\ddot{x}` | Double dot | | $\acute{x}$ | `\acute{x}` | Acute accent | | $\grave{x}$ | `\grave{x}` | Grave accent | | $\breve{x}$ | `\breve{x}` | Breve | | $\check{x}$ | `\check{x}` | Check mark | ## Font Styles {#sec-latex-fonts} | Symbol | Command | Description | |:------:|:--------|:------------| | $\mathbf{x}$ | `\mathbf{x}` | Bold (vectors/matrices) | | $\mathit{x}$ | `\mathit{x}` | Italic | | $\mathrm{x}$ | `\mathrm{x}` | Roman (upright) | | $\mathsf{x}$ | `\mathsf{x}` | Sans-serif | | $\mathtt{x}$ | `\mathtt{x}` | Typewriter | | $\mathcal{X}$ | `\mathcal{X}` | Calligraphic | | $\mathbb{R}$ | `\mathbb{R}` | Blackboard bold | | $\mathfrak{X}$ | `\mathfrak{X}` | Fraktur | | $\boldsymbol{\alpha}$ | `\boldsymbol{\alpha}` | Bold symbol (Greek) | ## Common Number Sets {#sec-latex-number-sets} | Symbol | Command | Description | |:------:|:--------|:------------| | $\mathbb{N}$ | `\mathbb{N}` | Natural numbers | | $\mathbb{Z}$ | `\mathbb{Z}` | Integers | | $\mathbb{Q}$ | `\mathbb{Q}` | Rational numbers | | $\mathbb{R}$ | `\mathbb{R}` | Real numbers | | $\mathbb{C}$ | `\mathbb{C}` | Complex numbers | | $\mathbb{P}$ | `\mathbb{P}` | Prime numbers | ## Brackets and Delimiters {#sec-latex-brackets} | Symbol | Command | Description | |:------:|:--------|:------------| | $(x)$ | `(x)` | Parentheses | | $[x]$ | `[x]` | Square brackets | | $\{x\}$ | `\{x\}` | Curly braces | | $\langle x \rangle$ | `\langle x \rangle` | Angle brackets | | $|x|$ | `|x|` | Vertical bars (absolute value) | | $\|x\|$ | `\|x\|` | Double bars (norm) | | $\lfloor x \rfloor$ | `\lfloor x \rfloor` | Floor | | $\lceil x \rceil$ | `\lceil x \rceil` | Ceiling | ### Auto-sizing Delimiters {#sec-latex-autosize} Use `\left` and `\right` for automatically sized delimiters: | Example | Code | |:--------|:-----| | $\left( \frac{a}{b} \right)$ | `\left( \frac{a}{b} \right)` | | $\left[ \sum_{i=1}^{n} x_i \right]$ | `\left[ \sum_{i=1}^{n} x_i \right]` | | $\left\{ \frac{a}{b} \right\}$ | `\left\{ \frac{a}{b} \right\}` | | $\left| \frac{a}{b} \right|$ | `\left| \frac{a}{b} \right|` | ## Matrix Environments {#sec-latex-matrices} | Environment | Result | Brackets | |:------------|:-------|:---------| | `matrix` | $\begin{matrix} a & b \\ c & d \end{matrix}$ | None | | `pmatrix` | $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ | Parentheses | | `bmatrix` | $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ | Square brackets | | `Bmatrix` | $\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}$ | Curly braces | | `vmatrix` | $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ | Vertical bars | | `Vmatrix` | $\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}$ | Double vertical | **Syntax:** ```latex $$\begin{bmatrix} a & b & c \\ d & e & f \end{bmatrix}$$ ``` ## Spacing {#sec-latex-spacing} | Command | Width | Example | |:--------|:------|:--------| | `\,` | 3/18 em (thin) | $a\,b$ | | `\:` | 4/18 em (medium) | $a\:b$ | | `\;` | 5/18 em (thick) | $a\;b$ | | `\quad` | 1 em | $a\quad b$ | | `\qquad` | 2 em | $a\qquad b$ | | `\!` | -3/18 em (negative) | $a\!b$ | ## Dots and Ellipses {#sec-latex-dots} | Symbol | Command | Usage | |:------:|:--------|:------| | $\ldots$ | `\ldots` | Baseline dots | | $\cdots$ | `\cdots` | Centered dots | | $\vdots$ | `\vdots` | Vertical dots | | $\ddots$ | `\ddots` | Diagonal dots | | $\cdot$ | `\cdot` | Single centered dot | ## Miscellaneous Symbols {#sec-latex-misc} | Symbol | Command | Description | |:------:|:--------|:------------| | $\infty$ | `\infty` | Infinity | | $\partial$ | `\partial` | Partial derivative | | $\nabla$ | `\nabla` | Nabla / Del | | $\prime$ | `\prime` | Prime | | $\angle$ | `\angle` | Angle | | $\triangle$ | `\triangle` | Triangle | | $\square$ | `\square` | Square | | $\circ$ | `\circ` | Circle / composition | | $\bullet$ | `\bullet` | Bullet | | $\star$ | `\star` | Star | | $\dagger$ | `\dagger` | Dagger | | $\ddagger$ | `\ddagger` | Double dagger | | $\ell$ | `\ell` | Script l | | $\hbar$ | `\hbar` | h-bar (Planck's constant) | | $\Re$ | `\Re` | Real part | | $\Im$ | `\Im` | Imaginary part | | $\aleph$ | `\aleph` | Aleph | ## Statistical Notation {#sec-latex-stats} | Expression | Code | Description | |:-----------|:-----|:------------| | $\bar{x}$ | `\bar{x}` | Sample mean | | $\hat{\mu}$ | `\hat{\mu}` | Estimated parameter | | $\tilde{x}$ | `\tilde{x}` | Median | | $X \sim N(\mu, \sigma^2)$ | `X \sim N(\mu, \sigma^2)` | Distribution | | ${n \choose k}$ | `{n \choose k}` | Binomial coefficient | | $\binom{n}{k}$ | `\binom{n}{k}` | Binomial coefficient (alternate) | | $P(A \mid B)$ | `P(A \mid B)` | Conditional probability | | $\mathbb{E}[X]$ | `\mathbb{E}[X]` | Expected value | | $\text{Var}(X)$ | `\text{Var}(X)` | Variance | | $\text{Cov}(X, Y)$ | `\text{Cov}(X, Y)` | Covariance | ## Common Statistical Formulas {#sec-latex-stat-formulas} ### Sample Statistics | Statistic | Formula | |:----------|:--------| | Sample mean | $\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$ | | Sample variance | $s^2 = \frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2$ | | Standard error | $SE = \frac{s}{\sqrt{n}}$ | | Z-score | $z = \frac{x - \mu}{\sigma}$ | ### Probability Distributions | Distribution | Probability Function | |:-------------|:--------------------| | Binomial | $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$ | | Poisson | $P(X=k) = \frac{e^{-\lambda}\lambda^k}{k!}$ | | Normal | $f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$ | | Exponential | $f(x) = \lambda e^{-\lambda x}$ | ## Equation Numbering in Quarto {#sec-latex-numbering} Add equation labels for cross-referencing: ```markdown $$ E = mc^2 $$ {#eq-einstein} See @eq-einstein for the mass-energy equivalence. ``` Multiple equations with alignment: ```markdown $$ \begin{aligned} y &= mx + b \\ &= 2x + 3 \end{aligned} $$ {#eq-line} ```