Functions, Symbols, and Special Characters

Basic Syntax

Type	LaTeX Source	Rendered Example
Inline Math	$...$	$...$
Display Math	`\[...\]`	$\displaystyle ...$
Superscripts and Subscripts	`\hat{x}{10}`	$\hat{x}{10}$
Superscripts and Subscripts	`a_{ij}`	$a_{ij}$
Fractions/Radicals	`\frac{a}{b}`	$\frac{a}{b}$
Fractions/Radicals	`\sqrt[n]{x}`	$\sqrt[n]{x}$
Automatically Sized Delimiters	`\left(`	$\left(\right.$
Automatically Sized Delimiters	`\right)`	$\left.\right)$
Display-Style Inline Fraction	`\dfrac{a}{b}`	$\dfrac{a}{b}$
Upright Characters	`\mathrm{e}`	$\mathrm{e}$

Equation Numbering

In LaTeX, you can use the \tag command to assign custom equation numbers. The following examples demonstrate how to add custom equation numbers in LaTeX:

Unnumbered Equations

Use $$ ... $$ or the [equation*] environment to create unnumbered equations.

% Unnumbered Equations

$$

\dot{V}(x) \leq -k_1 V(x)^{\frac{m}{n}} - k_2 V(x)^{\frac{r}{s}}

$$

Rendered output:

\dot{V}(x) \leq -k_1 V(x)^{\frac{m}{n}} - k_2 V(x)^{\frac{r}{s}}

Numbered Equations

Use the \tag{} command to assign a custom equation number, for example \tag{1.1}

% Equation with Custom Numbering

$$

\dot{V}(x) \leq -k_1 V(x)^{\frac{m}{n}} - k_2 V(x)^{\frac{r}{s}} \tag{1.1}

$$

Rendered output:

\dot{V}(x) \leq -k_1 V(x)^{\frac{m}{n}} - k_2 V(x)^{\frac{r}{s}} \tag{1.1}

Custom Numbering for Multiline Equations

In the align environment, you can assign a custom equation number to each line individually.

% Custom Numbering for Multiline Equations

\begin{align}

\dot{V}(x) &\leq -k_1 V(x)^{\frac{m}{n}} - k_2 V(x)^{\frac{r}{s}} \tag{1.2} \\

&\leq -k_1 V(x)^{\frac{m}{n}} \quad \text{(neglecting the sublinear term)} \tag{1.3}

\end{align}

\end{document}

Rendered output:

\begin{align} \dot{V}(x) &\leq -k_1 V(x)^{\frac{m}{n}} - k_2 V(x)^{\frac{r}{s}} \tag{1.2} \\ &\leq -k_1 V(x)^{\frac{m}{n}} \quad \text{(neglecting the sublinear term)} \tag{1.3} \end{align}

Notes:

The \tag{} command overrides the equation number generated automatically by LaTeX.
To reference custom equation numbers within equations, use \label{} together with \ref{}.

Accents / Diacritical Marks

LaTeX Source	Rendered Example
`\dot{a}`	$\dot{a}$
`\ddot{a}`	$\ddot{a}$
`\acute{a}`	$\acute{a}$
`\grave{a}`	$\grave{a}$
`\check{a}`	$\check{a}$
`\breve{a}`	$\breve{a}$
`\tilde{a}`	$\tilde{a}$
`\bar{a}`	$\bar{a}$
`\hat{a}`	$\hat{a}$
`\widehat{a}`	$\widehat{a}$
`\vec{a}`	$\vec{a}$

Standard Functions

Exponential Functions

LaTeX Source	Rendered Example
`\exp_a b = a^{b}`	$\exp_a b = a^{b}$
`\exp b = e^{b}`	$\exp b = e^{b}$
`10^{m}`	$10^{m}$

Logarithms

LaTeX Source	Rendered Example
`\ln c`	$\ln c$
`\lg d = \log e`	$\lg d = \log e$
`\log_{10} f`	$\log_{10} f$

Trigonometric Functions

LaTeX Source	Rendered Example
`\sin a`	$\sin a$
`\cos b`	$\cos b$
`\tan c`	$\tan c$
`\cot d`	$\cot d$
`\sec e`	$\sec e$
`\csc f`	$\csc f$
`\arcsin a`	$\arcsin a$
`\arccos b`	$\arccos b$
`\arctan c`	$\arctan c$
`\arccot d`	$\operatorname{arccot} d$
`\arcsec e`	$\operatorname{arcsec} e$
`\arccsc f`	$\operatorname{arccsc} f$
`\sinh a`	$\sinh a$
`\cosh b`	$\cosh b$
`\tanh c`	$\tanh c$
`\coth d`	$\coth d$
`\operatorname{sh}k`	$\operatorname{sh}k$
`\operatorname{ch}l`	$\operatorname{ch}l$
`\operatorname{th}m`	$\operatorname{th}m$
`\operatorname{coth}n`	$\operatorname{coth}n$
`\operatorname{argsh}o`	$\operatorname{argsh}o$
`\operatorname{argch}p`	$\operatorname{argch}p$
`\operatorname{argth}q`	$\operatorname{argth}q$

Sign Function and Absolute Value

LaTeX Source	Rendered Example
`\operatorname{sgn} r`	$\operatorname{sgn} r$
`\left\vert s \right\vert`	$\left\vert s \right\vert$

Maximum and Minimum

LaTeX Source	Rendered Example
`\min(x,y)`	$\min(x,y)$
`\max(x,y)`	$\max(x,y)$

Bounds and Limits

LaTeX Source	Rendered Example
`\min x`	$\min x$
`\max y`	$\max y$
`\inf s`	$\inf s$
`\sup t`	$\sup t$
`\lim u`	$\lim u$
`\liminf v`	$\liminf v$
`\limsup w`	$\limsup w$
`\lim_{n \to \infty} \frac{1}{n(n+1)}`	$\displaystyle\lim_{n \to \infty} \frac{1}{n(n+1)}$
`\dim p`	$\dim p$
`\deg q`	$\deg q$
`\det m`	$\det m$
`\ker\phi`	$\ker\phi$

Projections

LaTeX Source	Rendered Example
`\Pr j`	$\Pr j$
`\hom l`	$\hom l$
`\lVert z \rVert`	$\lVert z \rVert$
`\arg z`	$\arg z$

Differentials and Derivatives

LaTeX Source	Rendered Example
`dt`	$dt$
`\mathrm{d}t`	$\mathrm{d}t$
`\partial t`	$\partial t$
`\nabla\psi`	$\nabla\psi$
`dy/dx`	$dy/dx$
`\mathrm{d}y/\mathrm{d}x`	$\mathrm{d}y/\mathrm{d}x$
`\frac{dy}{dx}`	$\frac{dy}{dx}$
`\frac{\mathrm{d}y}{\mathrm{d}x}`	$\frac{\mathrm{d}y}{\mathrm{d}x}$
`\frac{\partial^2}{\partial x_1\partial x_2}y`	$\frac{\partial^2}{\partial x_1\partial x_2}y$
`\prime`	$\prime$
`\backprime`	$\backprime$
`f^\prime`	$f^\prime$
`f'`	$f'$
`f''`	$f''$
`f^{(3)}`	$f^{(3)}$
`\dot y`	$\dot y$
`\ddot y`	$\ddot y$

Letterlike Symbols and Constants

LaTeX Source	Rendered Example
`\infty`	$\infty$
`\aleph`	$\aleph$
`\complement`	$\complement$
`\backepsilon`	$\backepsilon$
`\eth`	$\eth$
`\Finv`	$\Finv$
`\hbar`	$\hbar$
`\Im`	$\Im$
`\imath`	$\imath$
`\jmath`	$\jmath$
`\Bbbk`	$\Bbbk$
`\ell`	$\ell$
`\mho`	$\mho$
`\wp`	$\wp$
`\Re`	$\Re$
`\circledS`	$\circledS$

Modular Arithmetic

LaTeX Source	Rendered Example
`s_k \equiv 0 \pmod{m}`	$s_k \equiv 0 \pmod{m}$
`a \bmod b`	$a \bmod b$
`\gcd(m, n), \operatorname{lcm}(m, n)`	$\gcd(m, n), \operatorname{lcm}(m, n)$
`\mid, \nmid, \shortmid, \nshortmid`	$\mid, \nmid, \shortmid, \nshortmid$

Radicals

LaTeX Source	Rendered Example
`\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}}`	$\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}}$

Operators

LaTeX Source	Rendered Example
`+, -, \pm, \mp, \dotplus`	$+, -, \pm, \mp, \dotplus$
`\times, \div, \divideontimes, /, \backslash`	$\times, \div, \divideontimes, /, \backslash$
`\cdot, * \ast, \star, \circ, \bullet`	$\cdot, * \ast, \star, \circ, \bullet$
`\boxplus, \boxminus, \boxtimes, \boxdot`	$\boxplus, \boxminus, \boxtimes, \boxdot$
`\oplus, \ominus, \otimes, \oslash, \odot`	$\oplus, \ominus, \otimes, \oslash, \odot$
`\circleddash, \circledcirc, \circledast`	$\circleddash, \circledcirc, \circledast$
`\bigoplus, \bigotimes, \bigodot`	$\bigoplus, \bigotimes, \bigodot$

Sets

LaTeX Source	Rendered Example
`\{ \}, \O \empty \emptyset, \varnothing`	$\{ \}, \text{\O} \empty \emptyset, \varnothing$
`\in, \notin \not\in, \ni, \not\ni`	$\in, \notin \not\in, \ni, \not\ni$
`\cap, \Cap, \sqcap, \bigcap`	$\cap, \Cap, \sqcap, \bigcap$
`\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus`	$\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus$
`\setminus, \smallsetminus, \times`	$\setminus, \smallsetminus, \times$
`\subset, \Subset, \sqsubset`	$\subset, \Subset, \sqsubset$
`\supset, \Supset, \sqsupset`	$\supset, \Supset, \sqsupset$
`\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq`	$\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq$
`\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq`	$\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq$
`\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq`	$\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq$
`\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq`	$\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq$

Relation Symbols

Geometric Symbols

LaTeX Source	Rendered Example
`\parallel, \nparallel, \shortparallel, \nshortparallel`	$\parallel, \nparallel, \shortparallel, \nshortparallel$
`\perp, \angle, \sphericalangle, \measuredangle, 45^\circ`	$\perp, \angle, \sphericalangle, \measuredangle, 45^\circ$
`\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar`	$\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar$
`\bigcirc, \triangle, \bigtriangleup, \bigtriangledown`	$\bigcirc, \triangle, \bigtriangleup, \bigtriangledown$
`\vartriangle, \triangledown`	$\vartriangle, \triangledown$
`\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright`	$\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright$

Logical Symbols

LaTeX Source	Rendered Example
`\forall, \exists, \nexists`	$\forall, \exists, \nexists$
`\therefore, \because, \And`	$\therefore, \because, \And$
`\lor \lor \vee, \curlyvee, \bigvee`	$\lor, \lor, \vee, \curlyvee, \bigvee$
`\land \land \wedge, \curlywedge, \bigwedge`	$\land, \land, \wedge, \curlywedge, \bigwedge$
`\bar{q}, \bar{abc}, \overline{q}, \overline{abc},`	$\bar{q}, \bar{abc}, \overline{q}, \overline{abc},$
`\lnot \neg, \not\operatorname{R}, \bot, \top`	$\lnot, \neg, \not\operatorname{R}, \bot, \top$
`\vdash \dashv, \vDash, \models`	$\vdash, \dashv, \vDash, \models$
`\Vdash \nvDash \nVdash \nvdash \nVDash`	$\Vdash, \nvDash, \nVdash, \nvdash, \nVDash$
`\ulcorner \urcorner \llcorner \lrcorner`	$\ulcorner \urcorner \llcorner \lrcorner$

Arrows

LaTeX Source	Rendered Example
`\Rightarrow, \Leftarrow`	$\Rightarrow, \Leftarrow$
`\Rightarrow, \nRightarrow, \Longrightarrow \implies`	$\Rightarrow, \nRightarrow, \Longrightarrow, \implies$
`\Leftarrow, \nLeftarrow, \Longleftarrow`	$\Leftarrow, \nLeftarrow, \Longleftarrow$
`\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff`	$\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff$
`\Uparrow, \Downarrow, \Updownarrow`	$\Uparrow, \Downarrow, \Updownarrow$
`\rightarrow \to, \nrightarrow, \longrightarrow`	$\rightarrow, \to, \nrightarrow, \longrightarrow$
`\leftarrow \gets, \nleftarrow, \longleftarrow`	$\leftarrow, \gets, \nleftarrow, \longleftarrow$
`\leftrightarrow, \nleftrightarrow, \longleftrightarrow`	$\leftrightarrow, \nleftrightarrow, \longleftrightarrow$
`\uparrow, \downarrow, \updownarrow`	$\uparrow, \downarrow, \updownarrow$
`\nearrow, \swarrow, \nwarrow, \searrow`	$\nearrow, \swarrow, \nwarrow, \searrow$
`\mapsto, \longmapsto`	$\mapsto, \longmapsto$
`\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons`	$\rightharpoonup, \rightharpoondown, \leftharpoonup, \leftharpoondown, \upharpoonleft, \upharpoonright, \downharpoonleft, \downharpoonright, \rightleftharpoons, \leftrightharpoons$
`\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright`	$\curvearrowleft, \circlearrowleft, \Lsh, \upuparrows, \rightrightarrows, \rightleftarrows, \rightarrowtail, \looparrowright$
`\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft`	$\curvearrowright, \circlearrowright, \Rsh, \downdownarrows, \leftleftarrows, \leftrightarrows, \leftarrowtail, \looparrowleft$
`\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow`	$\hookrightarrow, \hookleftarrow, \multimap, \leftrightsquigarrow, \rightsquigarrow, \twoheadrightarrow, \twoheadleftarrow$

Special Symbols

Ellipses: Two types of ellipses are commonly used in mathematical formulas. \ldots produces dots aligned with the text baseline, while \cdots produces dots aligned with the mathematical axis.

LaTeX Source	Rendered Example
`\amalg \% \dagger \ddagger \ldots \cdots`	$\amalg, \%, \dagger, \ddagger, \ldots, \cdots$
`\smile \frown \wr \triangleleft \triangleright`	$\smile, \frown, \wr, \triangleleft, \triangleright$
`\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp`	$\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp$

Miscellaneous

LaTeX Source	Rendered Example
`\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes`	$\diagup, \diagdown, \centerdot, \ltimes, \rtimes, \leftthreetimes, \rightthreetimes$
`\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq`	$\eqcirc, \circeq, \triangleq, \bumpeq, \Bumpeq, \doteqdot, \risingdotseq, \fallingdotseq$
`\intercal \barwedge \veebar \doublebarwedge \between \pitchfork`	$\intercal, \barwedge, \veebar, \doublebarwedge, \between, \pitchfork$
`\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright`	$\vartriangleleft, \ntriangleleft, \vartriangleright, \ntriangleright$
`\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq`	$\trianglelefteq, \ntrianglelefteq, \trianglerighteq, \ntrianglerighteq$

Superscripts, Subscripts, Integrals, and More

Function|Syntax|Output ^ denotes a superscript, and _ denotes a subscript. If a superscript or subscript contains more than one character, enclose the characters in {} to group them. Superscripts and subscripts can be nested or used together.

Function	LaTeX Source	Rendered Example
Superscript	`a^2`	$a^2$
Subscript	`a_2`	$a_2$
Grouping	`a^{2+2}`	$a^{2+2}$
Grouping	`a_{i,j}`	$a_{i,j}$
Combined Superscripts and Subscripts	`x_2^3`	$x_2^3$
Prescripts	`{}_1^2\!X_3^4`	${}_1^2\!X_3^4$
Derivative (HTML)	`x'`	$x'$
Derivative (PNG)	`x^\prime`	$x^\prime$
Derivative (Incorrect)	`x\prime`	$x\prime$
Dot Notation for Derivatives	`\dot{x}`	$\dot{x}$
Dot Notation for Derivatives	`\ddot{y}`	$\ddot{y}$
Vector	`\vec{c}`(single letter only)	$\vec{c}$
Vector	`\overleftarrow{a b}`	$\overleftarrow{a b}$
Vector	`\overrightarrow{c d}`	$\overrightarrow{c d}$
Vector	`\overleftrightarrow{a b}`	$\overleftrightarrow{a b}$
Vector	`\widehat{e f g}`	$\widehat{e f g}$
Overarc	`\overset{\frown}{AB}`	$\overset{\frown}{AB}$
Overline	`\overline{h i j}`	$\overline{h i j}$
Underline	`\underline{k l m}`	$\underline{k l m}$
Summation	`\sum_{k=1}^N k^2`	$\displaystyle\sum_{k=1}^N k^2$
Summation	`\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}`	$\begin{matrix} \displaystyle\sum_{k=1}^N k^2 \end{matrix}$
Product	`\prod_{i=1}^N x_i`	$\prod_{i=1}^N x_i$
Product	`\begin{matrix} \prod_{i=1}^N x_i \end{matrix}`	$\begin{matrix} \displaystyle\prod_{i=1}^N x_i \end{matrix}$
Coproduct	`\coprod_{i=1}^N x_i`	$\coprod_{i=1}^N x_i$
Coproduct	`\begin{matrix} \coprod_{i=1}^N x_i\end{matrix}`	$\begin{matrix} \displaystyle\coprod_{i=1}^N x_i\end{matrix}$
Limit	`\lim_{n \to \infty}x_n`	$\displaystyle\lim_{n \to \infty}x_n$
Limit	`\begin{matrix} \lim_{n \to \infty}x_n \end{matrix}`	$\begin{matrix} \displaystyle\lim_{n \to \infty}x_n \end{matrix}$
Integral	`\int_{-N}^{N} e^x\, \mathrm{d}x`	$\displaystyle\int_{-N}^{N} e^x\, \mathrm{d}x$
Integral	`\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}`	$\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}$
Double Integral	`\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y`	$\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y$
Triple Integral	`\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z`	$\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$
Closed Contour and Surface Integrals	`\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y`	$\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y$
Intersection	`\bigcap_{i=1}^{n} p`	$\displaystyle\bigcap_{i=1}^{n} p$
Union	`\bigcup_{i=1}^{k} p`	$\displaystyle\bigcup_{i=1}^{k} p$

Fractions

Use the \frac{numerator}{denominator} command to create a fraction. Fractions can be nested. For a simple fraction, enter \frac ab to quickly produce $\frac ab$ . For a complex fractional expression, you can also use numerator \over denominator to create a single-level fraction.

Function	LaTeX Source	Rendered Example
Fraction	`\frac{2}{4}=0.5`	$\frac{2}{4}=0.5$
Small Fraction	`\tfrac{2}{4} = 0.5`	$\tfrac{2}{4} = 0.5$
Continued Fraction (Large Nested Fraction)	`\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a`	$\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a$
Large Non-Nested Fraction	`\dfrac{2}{4} = 0.5 \quad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a`	$\dfrac{2}{4} = 0.5 \quad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a$
Binomial Coefficient	`\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}`	$\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$
Small Binomial Coefficient	`\tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}`	$\tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$
Large Binomial Coefficient	`\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}`	$\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$

Avoid using \frac in base-e exponential functions, limits, and integrals: it can make the expression look awkward and may introduce ambiguity. For this reason, it is rarely used in these contexts in professional mathematical typesetting. Write these fractions horizontally, using a slash / instead of a fraction bar.

\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \\
\hline \\
e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\
\int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\
\end{array}

Rendered output:

\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ e^{i\frac{\pi}{2}} \quad e^{\frac{i\pi}{2}} & e^{i\pi/2} \\ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}

Note: In exponents and integrals, professional typesetting recommends using a slash / instead of \frac for a more concise and visually balanced formula.

Matrices, Piecewise Expressions, and Systems of Equations

Syntax:

\begin{type}
formula content
\end{type}

The type can be a matrix environment (matrix pmatrix bmatrix Bmatrix vmatrix Vmatrix), a piecewise expression (cases), multiline aligned equations (aligned), or an array (array).

Within the formula, insert & in each row to specify alignment points, and use \\ at the end of each row to start a new line.

Matrices without Delimiters

\begin{matrix}
x & y \\
z & v
\end{matrix}

Rendered output:

\begin{matrix} x & y \\ z & v \end{matrix}

Matrices with Delimiters

\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}

Rendered output:

\begin{vmatrix} x & y \\ z & v \end{vmatrix}

\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}

Rendered output:

\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}

Use \cdots, \ddots, and \vdots to insert ellipses.

\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}

Rendered output:

\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}

\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}

Rendered output:

\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}

\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}

Rendered output:

\begin{pmatrix} x & y \\ z & v \end{pmatrix}

Piecewise Expressions

f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}

Rendered output:

f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}

Multiline Equations and Congruences

To arrange a sequence of equations in a neatly aligned, centered column, use \begin{aligned}...\end{aligned}.

\begin{aligned}
f(x) &= (m+n)^2 \\
&= m^2+2mn+n^2
\end{aligned}

Rendered output:

\begin{aligned} f(x) &= (m+n)^2 \\ &= m^2+2mn+n^2 \end{aligned}

\begin{aligned}
3^{6n+3}+4^{6n+3}
&\equiv (3^3)^{2n+1}+(4^3)^{2n+1}\\
&\equiv 27^{2n+1}+64^{2n+1}\\
&\equiv 27^{2n+1}+(-27)^{2n+1}\\
&\equiv 27^{2n+1}-27^{2n+1}\\
&\equiv 0 \pmod{91}\\
\end{aligned}

Rendered output:

\begin{aligned} 3^{6n+3}+4^{6n+3} &\equiv (3^3)^{2n+1}+(4^3)^{2n+1}\\ &\equiv 27^{2n+1}+64^{2n+1}\\ &\equiv 27^{2n+1}+(-27)^{2n+1}\\ &\equiv 27^{2n+1}-27^{2n+1}\\ &\equiv 0 \pmod{91}\\ \end{aligned}

\begin{alignedat}{3}
f(x) &= (m-n)^2 \\
f(x) &= (-m+n)^2 \\
&= m^2-2mn+n^2
\end{alignedat}

Rendered output:

\begin{alignedat}{3} f(x) &= (m-n)^2 \\ f(x) &= (-m+n)^2 \\ &= m^2-2mn+n^2 \end{alignedat}

Systems of Equations

\begin{cases}
\begin{split}
p &= P(y=1|\mathbf{x})=
\frac{1}{1+e^{-\theta^T\mathbf{X}}}\\
1-p &= P(y=0|\mathbf{x})=1-P(y=1|\mathbf{x})=
\frac{1}{1+e^{\theta^T\mathbf{X}}}
\end{split}
\end{cases}

Rendered output:

\begin{cases} \begin{split} p &= P(y=1|\mathbf{x})= \frac{1}{1+e^{-\theta^T\mathbf{X}}}\\ 1-p &= P(y=0|\mathbf{x})=1-P(y=1|\mathbf{x})= \frac{1}{1+e^{\theta^T\mathbf{X}}} \end{split} \end{cases}

Note that LaTeX environments can be nested. The example above uses \begin{cases} \end{cases} to enclose \begin{split} \end{split}. You can also combine formulas with text, for example:

\text{Decision Boundary}=
\begin{cases}
    1\quad \text{if }\ \hat{y}>0.5\\
    0\quad \text{otherwise}
\end{cases}

Rendered output:

\text{Decision Boundary}= \begin{cases} 1\quad \text{if }\ \hat{y}>0.5\\ 0\quad \text{otherwise} \end{cases}

Example

\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}

Rendered output:

\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}

\left\{\begin{aligned}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{aligned}\right.

Rendered output:

\left\{\begin{aligned} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{aligned}\right.

Arrays and Tables

A formatted table is generally easier to read than plain or typeset text alone. Arrays and tables begin with \begin{array}, followed by a specification of the number of columns and their text alignment. The specifiers c, l, and r indicate centered, left-aligned, and right-aligned columns, respectively. To insert a vertical rule, add | to the column specification; to insert a horizontal rule, add \hline before the next row. As with matrices, separate entries within each row using &, end each row with \\, and close the array with \end{array}.

\begin{array}{c|lcr}
n & \text{Left-aligned} & \text{Centered} & \text{Right-aligned} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}

Rendered output:

\begin{array}{c|lcr} n & \text{Left-aligned} & \text{Centered} & \text{Right-aligned} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}

\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}

Rendered output:

\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}

Rendered output:

\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

\begin{array}{ccc}
a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0
\end{array}

Rendered output:

\begin{array}{ccc} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0 \end{array}

Nested Arrays or Tables

Multiple arrays or tables can be nested to form a group of arrays or tables. Declare the $$ delimiters before using nested arrays or tables.

% outer vertical array of arrays (outer vertical table)
\begin{array}{c}
    % inner horizontal array of arrays (inner horizontal table)
    \begin{array}{cc}
        % inner array of minimum values (inner array of minimum values)
        \begin{array}{c|cccc}
        \text{min} & 0 & 1 & 2 & 3\\
        \hline
        0 & 0 & 0 & 0 & 0\\
        1 & 0 & 1 & 1 & 1\\
        2 & 0 & 1 & 2 & 2\\
        3 & 0 & 1 & 2 & 3
        \end{array}
        &
        % inner array of maximum values (inner array of maximum values)
        \begin{array}{c|cccc}
        \text{max}&0&1&2&3\\
        \hline
        0 & 0 & 1 & 2 & 3\\
        1 & 1 & 1 & 2 & 3\\
        2 & 2 & 2 & 2 & 3\\
        3 & 3 & 3 & 3 & 3
        \end{array}
    \end{array}
    \\ % End of the first inner row of tables
    % inner array of delta values (second inner row: delta values)
    \begin{array}{c|cccc}
        \Delta&0&1&2&3\\
        \hline
        0 & 0 & 1 & 2 & 3\\
        1 & 1 & 0 & 1 & 2\\
        2 & 2 & 1 & 0 & 1\\
        3 & 3 & 2 & 1 & 0
    \end{array}
\end{array}

Rendered output:

\begin{array}{c} \begin{array}{cc} \begin{array}{c|cccc} \text{min} & 0 & 1 & 2 & 3\\ \hline 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 1\\ 2 & 0 & 1 & 2 & 2\\ 3 & 0 & 1 & 2 & 3 \end{array} & \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 \end{array} \end{array} \\ \begin{array}{c|cccc} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} \end{array}

Matrices with Separators Using Arrays

& separates entries, and \\ starts a new line

\left[
\begin{array}{cc|c}
1&2&3\\
4&5&6
\end{array}
\right]

Rendered output:

\left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array} \right]

Fonts

To change the font of selected characters in a formula, use {\font {characters to format}}, replacing \font with an appropriate font command from the table below. Mathematical formulas generally use italic type by default.

Greek Letters

Category	Source	Rendered Output
Uppercase Greek Letters 1	`\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta`	$\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta$
Uppercase Greek Letters 2	`\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi`	$\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi$
Uppercase Greek Letters 3	`\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega`	$\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega$
Lowercase Greek Letters 1	`\alpha \beta \gamma \delta \epsilon \zeta \eta \theta`	$\alpha \beta \gamma \delta \epsilon \zeta \eta \theta$
Lowercase Greek Letters 2	`\iota \kappa \lambda \mu \nu \omicron \xi \pi`	$\iota \kappa \lambda \mu \nu \omicron \xi \pi$
Lowercase Greek Letters 3	`\rho \sigma \tau \upsilon \phi \chi \psi \omega`	$\rho \sigma \tau \upsilon \phi \chi \psi \omega$
Variant Greek Letters 1	`\varepsilon \digamma \varkappa \varpi`	$\varepsilon \digamma \varkappa \varpi$
Variant Greek Letters 2	`\varrho \varsigma \vartheta \varphi`	$\varrho \varsigma \vartheta \varphi$

Hebrew Symbols

Source	Rendered Output
`\aleph \beth \gimel \daleth`	$\aleph \beth \gimel \daleth$

Font Command Shorthands

Input	Description	Output	Input	Description	Output
`\rm`	Roman	$\mathrm{Sample}$	`\cal`	Calligraphic	$\mathcal{SAMPLE}$
`\it`	Italic	$\mathit{Sample}$	`\Bbb`	Blackboard Bold	$\mathbb{SAMPLE}$
`\bf`	Bold	$\mathbf{Sample}$	`\mathit`	Math Italic	$\mathit{SAMPLE}$
`\sf`	Sans Serif	$\mathsf{Sample}$	`\scr`	Script	$\mathscr{SAMPLE}$
`\tt`	Typewriter	$\mathtt{Sample}$	`\frak`	Fraktur	$\mathfrak{Sample}$

All Fonts

Blackboard Bold `\mathbb{}`

Source	Rendered Output
`\mathbb{ABCDEFGHI}`	$\mathbb{ABCDEFGHI}$
`\mathbb{JKLMNOPQR}`	$\mathbb{JKLMNOPQR}$
`\mathbb{STUVWXYZ}`	$\mathbb{STUVWXYZ}$

Bold `\mathbf{}`

Source	Rendered Output
`\mathbf{ABCDEFGHI}`	$\mathbf{ABCDEFGHI}$
`\mathbf{JKLMNOPQR}`	$\mathbf{JKLMNOPQR}$
`\mathbf{STUVWXYZ}`	$\mathbf{STUVWXYZ}$
`\mathbf{abcdefghijklm}`	$\mathbf{abcdefghijklm}$
`\mathbf{nopqrstuvwxyz}`	$\mathbf{nopqrstuvwxyz}$
`\mathbf{0123456789}`	$\mathbf{0123456789}$

Bold Greek Letters `\boldsymbol{}`

Source	Rendered Output
`\boldsymbol{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}`	$\boldsymbol{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}$
`\boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}`	$\boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}$
`\boldsymbol{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}`	$\boldsymbol{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}$
`\boldsymbol{\alpha \beta \gamma \delta \epsilon \zeta \eta \theta}`	$\boldsymbol{\alpha \beta \gamma \delta \epsilon \zeta \eta \theta}$
`\boldsymbol{\iota \kappa \lambda \mu \nu \omicron \xi \pi}`	$\boldsymbol{\iota \kappa \lambda \mu \nu \omicron \xi \pi}$
`\boldsymbol{\sigma \tau \upsilon \phi \chi \psi \omega}`	$\boldsymbol{\sigma \tau \upsilon \phi \chi \psi \omega}$
`\boldsymbol{\varepsilon \digamma \varkappa \varpi}`	$\boldsymbol{\varepsilon \digamma \varkappa \varpi}$
`\boldsymbol{\varrho \varsigma \vartheta \varphi}`	$\boldsymbol{\varrho \varsigma \vartheta \varphi}$

Italic (Default for Latin Letters)`\mathit{}`

Source	Rendered Output
`\mathit{0123456789}`	$\mathit{0123456789}$

Italic Greek Letters (Default for Lowercase Letters)`\mathit{}`

Source	Rendered Output
`\mathit{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}`	$\mathit{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}$
`\mathit{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}`	$\mathit{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}$
`\mathit{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}`	$\mathit{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}$

Roman `\mathrm{}`

Source	Rendered Output
`\mathrm{ABCDEFGHI}`	$\mathrm{ABCDEFGHI}$
`\mathrm{JKLMNOPQR}`	$\mathrm{JKLMNOPQR}$
`\mathrm{STUVWXYZ}`	$\mathrm{STUVWXYZ}$
`\mathrm{abcdefghijklm}`	$\mathrm{abcdefghijklm}$
`\mathrm{nopqrstuvwxyz}`	$\mathrm{nopqrstuvwxyz}$
`\mathrm{0123456789}`	$\mathrm{0123456789}$

Sans Serif `\mathsf{}`

Source	Rendered Output
`\mathsf{ABCDEFGHI}`	$\mathsf{ABCDEFGHI}$
`\mathsf{JKLMNOPQR}`	$\mathsf{JKLMNOPQR}$
`\mathsf{STUVWXYZ}`	$\mathsf{STUVWXYZ}$
`\mathsf{abcdefghijklm}`	$\mathsf{abcdefghijklm}$
`\mathsf{nopqrstuvwxyz}`	$\mathsf{nopqrstuvwxyz}$
`\mathsf{0123456789}`	$\mathsf{0123456789}$

Sans Serif Greek Letters (Uppercase Only)`\mathsf{}`

Source	Rendered Output
`\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}`	$\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}$
`\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}`	$\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}$
`\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}`	$\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}$

Script / Calligraphic `\mathcal{}`

Source	Rendered Output
`\mathcal{ABCDEFGHI}`	$\mathcal{ABCDEFGHI}$
`\mathcal{JKLMNOPQR}`	$\mathcal{JKLMNOPQR}$
`\mathcal{STUVWXYZ}`	$\mathcal{STUVWXYZ}$

Fraktur `\mathfrak{}`

Source	Rendered Output
`\mathfrak{ABCDEFGHI}`	$\mathfrak{ABCDEFGHI}$
`\mathfrak{JKLMNOPQR}`	$\mathfrak{JKLMNOPQR}$
`\mathfrak{STUVWXYZ}`	$\mathfrak{STUVWXYZ}$
`\mathfrak{abcdefghijklm}`	$\mathfrak{abcdefghijklm}$
`\mathfrak{nopqrstuvwxyz}`	$\mathfrak{nopqrstuvwxyz}$
`\mathfrak{0123456789}`	$\mathfrak{0123456789}$

Lowercase Script `\mathscr{}`

Source	Rendered Output
`\mathscr{abcdefghijklm}`	$\mathscr{abcdefghijklm}$

Mixed Fonts

Feature	Syntax	Rendered Output
Italic Characters (Spaces Ignored)	`x y z`	$x y z$
Upright Characters	`\text{x y z}`	$\text{x y z}$
Mixed Italic and Upright Text (Poor)	`\text{if} n \text{is even}`	$\text{if} n \text{is even}$
Mixed Italic and Upright Text (Good)	`\text{if } n\text{ is even}`	$\text{if } n\text{ is even}$
Mixed Italic and Upright Text (Alternative: `\` Forces a Space)	`\text{if}\ n \text{is even}`	$\text{if}\ n \text{is even}$

Explanatory Text

Use \text{text} to add explanatory text (the text is not interpreted as a mathematical formula and is not italicized). You can still insert formulas inside \text{text} using $formula$ .

Example:

f(n)= \begin{cases}
n/2, & \text{if } n \text{ is even} \\
3n+1, & \text{if }n \text{ is odd}
\end{cases}

Rendered output:

f(n)= \begin{cases} n/2, & \text{if } n \text{ is even} \\ 3n+1, & \text{if }n \text{ is odd} \end{cases}

Delimiters

(), [], and | represent the symbols themselves. Use \{ \} to display {}.

Function	Syntax	Output
Short Delimiters	`\frac{1}{2}`	$\frac{1}{2}$
Tall Delimiters	`\left(\frac{1}{2} \right)`	$\left(\frac{1}{2} \right)$
Round Brackets (Parentheses)	`\left( \frac{a}{b} \right)`	$\left( \frac{a}{b} \right)$
Square Brackets	`\left[ \frac{a}{b} \right]`	$\left[ \frac{a}{b} \right]$
Curly Braces	`\left\{ \frac{a}{b} \right\}`	$\left\{ \frac{a}{b} \right\}$
Angle Brackets	`\left \langle \frac{a}{b} \right \rangle`	$\left \langle \frac{a}{b} \right \rangle$
Single Vertical Bars (Absolute Value)	`\left\vert \frac{a}{b} \right\vert`	$\left\vert \frac{a}{b} \right\vert$
Double Vertical Bars (Norm)	`\left\Vert \frac{a}{b} \right\Vert`	$\left\Vert \frac{a}{b} \right\Vert$
Floor Function	`\left \lfloor \frac{a}{b} \right \rfloor`	$\left \lfloor \frac{a}{b} \right \rfloor$
Ceiling Function	`\left \lceil \frac{c}{d} \right \rceil`	$\left \lceil \frac{c}{d} \right \rceil$
Slash and Backslash	`\left / \frac{a}{b} \right \backslash`	$\left / \frac{a}{b} \right \backslash$
Up and Down Arrows	`\left \uparrow \frac{a}{b} \right \downarrow`	$\left \uparrow \frac{a}{b} \right \downarrow$
Double-Line Up and Down Arrows (Automatically Sized Delimiters)	`\left \Uparrow \frac{a}{b} \right \Downarrow`	$\left \Uparrow \frac{a}{b} \right \Downarrow$
Single-Line and Double-Line Bidirectional Vertical Arrows	`\left \updownarrow \frac{a}{b} \right \Updownarrow`	$\left \updownarrow \frac{a}{b} \right \Updownarrow$
Mixed Delimiters	`\left[ 0,1 \right)`	$\left[ 0,1 \right)$
Mixed Delimiters	`\left \langle \psi \right \|`	$\left \langle \psi \right \vert$
Overbrace	`\overbrace{1+2+\cdots+100}`	$\overbrace{1+2+\cdots+100}$
Overbrace	`\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}`	$\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}$
Underbrace	`\underbrace{a+b+\cdots+z}`	$\underbrace{a+b+\cdots+z}$
Underbrace	`\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}`	$\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}$

Use \left and \right to create automatically sized (parentheses), [square brackets], and {braces}. If only one delimiter is needed, use \left. or \right. for the other side.

Function	Syntax	Output
Left Delimiter Only	`\left\{\frac{a}{b} \right.`	$\left\{\frac{a}{b} \right.$
Right Delimiter Only	`\left. \frac{a}{b} \right\}`	$\left. \frac{a}{b} \right\}$

Note: Use \big, \Big, \bigg, \Bigg to control delimiter sizes, as in the following code \Bigg ( \bigg [ \Big \langle \big \| \frac{a}{b} \big \| \Big \rangle \bigg ] \Bigg )

Rendered output: $\Bigg ( \bigg [ \Big \langle \big \| \frac{a}{b} \big \| \Big \rangle \bigg ] \Bigg )$

Spacing

KaTeX handles most spacing automatically, but sometimes manual control is needed.

Function	Syntax	Output	Description
Two Quad Spaces	`A\qquad B`	$A\qquad B$	Two M-widths
Quad Space	`A\quad B`	$A\quad B$	One M-width
Large Space	`A\ B`	$A\ B$	1/3 M-width
Medium Space	`A\;B`	$A\;B$	2/7 M-width
Small Space	`A\,B`	$A\,B$	1/6 M-width
Negative Thin Space	`\alpha\!\beta`	$\alpha\!\beta$	Minus 1/6 M-width
No Space	`\alpha\beta`	$\alpha\beta$	0

Text Colors in LaTeX

Use \color{color}{text} to change the color of specific text. Text coloring requires browser support; if the browser does not support the specified color, the text is rendered in black.

Colors Supported by Older Browsers

Input	Output	Input	Output
`black`	$\color{black}{text}$	`grey`	$\color{grey}{text}$
`silver`	$\color{silver}{text}$	`white`	$\color{white}{text}$
`maroon`	$\color{maroon}{text}$	`red`	$\color{red}{text}$
`yellow`	$\color{yellow}{text}$	`lime`	$\color{lime}{text}$
`olive`	$\color{olive}{text}$	`green`	$\color{green}{text}$
`teal`	$\color{teal}{text}$	`aqua`	$\color{aqua}{text}$
`blue`	$\color{blue}{text}$	`navy`	$\color{navy}{text}$
`purple`	$\color{purple}{text}$	`fuchsia`	$\color{fuchsia}{text}$

Custom RGB Colors

In newer browsers, you can customize text colors using hexadecimal color values.

Syntax:

\color{#rgb}{text}

Here, r, g, and b each take a value from 0-9 or a-f.

Example:

\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & & &
\verb+#00F+ & \color{#00F}{text} & & \\
& & \verb+#0F0+ & \color{#0F0}{text} &
& & \verb+#0FF+ & \color{#0FF}{text}\\
\verb+#F00+ & \color{#F00}{text} & & &
\verb+#F0F+ & \color{#F0F}{text} & & \\
& & \verb+#FF0+ & \color{#FF0}{text} &
& & \verb+#FFF+ & \color{#FFF}{text}\\
\hline
\end{array}

Rendered output:

\begin{array}{|rrrrrrrr|}\hline \verb+#000+ & \color{#000}{text} & & & \verb+#00F+ & \color{#00F}{text} & & \\ & & \verb+#0F0+ & \color{#0F0}{text} & & & \verb+#0FF+ & \color{#0FF}{text}\\ \verb+#F00+ & \color{#F00}{text} & & & \verb+#F0F+ & \color{#F0F}{text} & & \\ & & \verb+#FF0+ & \color{#FF0}{text} & & & \verb+#FFF+ & \color{#FFF}{text}\\ \hline \end{array}

Example:

\begin{array}{|rrrrrrrr|}
\hline
\verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text}  \\
\verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text}  \\
\verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text}  \\
\verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text}  \\
\hline
\verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text}  \\
\verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text}  \\
\verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text}  \\
\verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text}  \\
\hline
\verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text}  \\
\verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text}  \\
\verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text}  \\
\verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text}  \\
\hline
\end{array}

Rendered output:

\begin{array}{|rrrrrrrr|}\hline \verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text} \\ \verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text} \\ \verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text} \\ \verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text} \\ \hline \verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text} \\ \verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text} \\ \verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text} \\ \verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text} \\ \hline \verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text} \\ \verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text} \\ \verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text} \\ \verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text} \\ \hline \end{array}

Supported Color Palette

Color	Color	Color	Color
$\color{Apricot}{Apricot}$	$\color{Aquamarine}{Aquamarine}$	$\color{Bittersweet}{Bittersweet}$	$\color{Black}{Black}$
$\color{Blue}{Blue}$	$\color{BlueGreen}{BlueGreen}$	$\color{BlueViolet}{BlueViolet}$	$\color{BrickRed}{BrickRed}$
$\color{Brown}{Brown}$	$\color{BurntOrange}{BurntOrange}$	$\color{CadetBlue}{CadetBlue}$	$\color{CarnationPink}{CarnationPink}$
$\color{Cerulean}{Cerulean}$	$\color{CornflowerBlue}{CornflowerBlue}$	$\color{Cyan}{Cyan}$	$\color{Dandelion}{Dandelion}$
$\color{DarkOrchid}{DarkOrchid}$	$\color{Emerald}{Emerald}$	$\color{ForestGreen}{ForestGreen}$	$\color{Fuchsia}{Fuchsia}$
$\color{Goldenrod}{Goldenrod}$	$\color{Gray}{Gray}$	$\color{Green}{Green}$	$\color{GreenYellow}{GreenYellow}$
$\color{JungleGreen}{JungleGreen}$	$\color{Lavender}{Lavender}$	$\color{LimeGreen}{LimeGreen}$	$\color{Magenta}{Magenta}$
$\color{Mahogany}{Mahogany}$	$\color{Maroon}{Maroon}$	$\color{Melon}{Melon}$	$\color{MidnightBlue}{MidnightBlue}$
$\color{Mulberry}{Mulberry}$	$\color{NavyBlue}{NavyBlue}$	$\color{OliveGreen}{OliveGreen}$	$\color{Orange}{Orange}$
$\color{OrangeRed}{OrangeRed}$	$\color{Orchid}{Orchid}$	$\color{Peach}{Peach}$	$\color{Periwinkle}{Periwinkle}$
$\color{PineGreen}{PineGreen}$	$\color{Plum}{Plum}$	$\color{ProcessBlue}{ProcessBlue}$	$\color{Purple}{Purple}$
$\color{RawSienna}{RawSienna}$	$\color{Red}{Red}$	$\color{RedOrange}{RedOrange}$	$\color{RedViolet}{RedViolet}$
$\color{Rhodamine}{Rhodamine}$	$\color{RoyalBlue}{RoyalBlue}$	$\color{RoyalPurple}{RoyalPurple}$	$\color{RubineRed}{RubineRed}$
$\color{Salmon}{Salmon}$	$\color{SeaGreen}{SeaGreen}$	$\color{Sepia}{Sepia}$	$\color{SkyBlue}{SkyBlue}$
$\color{SpringGreen}{SpringGreen}$	$\color{Tan}{Tan}$	$\color{TealBlue}{TealBlue}$	$\color{Thistle}{Thistle}$
$\color{Turquoise}{Turquoise}$	$\color{Violet}{Violet}$	$\color{VioletRed}{VioletRed}$	$\color{WildStrawberry}{WildStrawberry}$
$\color{Yellow}{Yellow}$	$\color{YellowGreen}{YellowGreen}$	$\color{YellowOrange}{YellowOrange}$

Note: Color names must begin with an uppercase letter, for example \color{OliveGreen}{text}.

Examples

{\color{Blue}x^2}+{\color{Brown}2x} - {\color{OliveGreen}1} ${\color{Blue}x^2}+{\color{Brown}2x} - {\color{OliveGreen}1}$

x_{\color{Maroon}1,2}=\frac{-b\pm\sqrt{{\color{Maroon}b^2-4ac}}}{2a} $x_{\color{Maroon}{1,2}}=\dfrac{-b\pm\sqrt{\color{Maroon}{b^2-4ac}}}{2a}$

LaTeX Source	Rendered Example
`=, \ne, \neq, \equiv, \not\equiv`	$=, \ne, \neq, \equiv, \not\equiv$
`\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=`	$\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=$
`\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong`	$\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong$
`\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto`	$\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto$
`<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot`	$<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot$
`>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot`	$>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot$
`\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq`	$\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq$
`\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq`	$\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq$
`\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless`	$\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless$
`\leqslant, \nleqslant, \eqslantless`	$\leqslant, \nleqslant, \eqslantless$
`\geqslant, \ngeqslant, \eqslantgtr`	$\geqslant, \ngeqslant, \eqslantgtr$
`\lesssim, \lnsim, \lessapprox, \lnapprox`	$\lesssim, \lnsim, \lessapprox, \lnapprox$
`\gtrsim, \gnsim, \gtrapprox, \gnapprox`	$\gtrsim, \gnsim, \gtrapprox, \gnapprox$
`\prec, \nprec, \preceq, \npreceq, \precneqq`	$\prec, \nprec, \preceq, \npreceq, \precneqq$
`\succ, \nsucc, \succeq, \nsucceq, \succneqq`	$\succ, \nsucc, \succeq, \nsucceq, \succneqq$
`\preccurlyeq, \curlyeqprec`	$\preccurlyeq, \curlyeqprec$
`\succcurlyeq, \curlyeqsucc`	$\succcurlyeq, \curlyeqsucc$
`\precsim, \precnsim, \precapprox, \precnapprox`	$\precsim, \precnsim, \precapprox, \precnapprox$
`\succsim, \succnsim, \succapprox, \succnapprox`	$\succsim, \succnsim, \succapprox, \succnapprox$

Basic Syntax​

Equation Numbering​

Unnumbered Equations​

Numbered Equations​

Custom Numbering for Multiline Equations​

Accents / Diacritical Marks​

Standard Functions​

Exponential Functions​

Logarithms​

Trigonometric Functions​

Sign Function and Absolute Value​

Maximum and Minimum​

Bounds and Limits​

Projections​

Differentials and Derivatives​

Letterlike Symbols and Constants​

Modular Arithmetic​

Radicals​

Operators​

Sets​

Relation Symbols​

Geometric Symbols​

Logical Symbols​

Arrows​

Special Symbols​

Miscellaneous​

Superscripts, Subscripts, Integrals, and More​

Fractions​

Matrices, Piecewise Expressions, and Systems of Equations

Matrices without Delimiters​

Matrices with Delimiters​

Piecewise Expressions​

Multiline Equations and Congruences​

Systems of Equations​

Arrays and Tables

Nested Arrays or Tables​

Matrices with Separators Using Arrays​

Fonts

Greek Letters​

Hebrew Symbols​

Font Command Shorthands​

All Fonts​

Blackboard Bold \mathbb{}​

Bold \mathbf{}​

Bold Greek Letters \boldsymbol{}​

Italic (Default for Latin Letters)\mathit{}​

Italic Greek Letters (Default for Lowercase Letters)\mathit{}​

Roman \mathrm{}​

Sans Serif \mathsf{}​

Sans Serif Greek Letters (Uppercase Only)\mathsf{}​

Script / Calligraphic \mathcal{}​

Fraktur \mathfrak{}​

Lowercase Script \mathscr{}​

Mixed Fonts​

Explanatory Text​

Delimiters​

Spacing​

Text Colors in LaTeX

Colors Supported by Older Browsers​

Custom RGB Colors​

Supported Color Palette​

Examples​

Basic Syntax

Equation Numbering

Unnumbered Equations

Numbered Equations

Custom Numbering for Multiline Equations

Accents / Diacritical Marks

Standard Functions

Exponential Functions

Logarithms

Trigonometric Functions

Sign Function and Absolute Value

Maximum and Minimum

Bounds and Limits

Projections

Differentials and Derivatives

Letterlike Symbols and Constants

Modular Arithmetic

Radicals

Operators

Sets

Relation Symbols

Geometric Symbols

Logical Symbols

Arrows

Special Symbols

Miscellaneous

Superscripts, Subscripts, Integrals, and More

Fractions

Matrices without Delimiters

Matrices with Delimiters

Piecewise Expressions

Multiline Equations and Congruences

Systems of Equations

Nested Arrays or Tables

Matrices with Separators Using Arrays

Greek Letters

Hebrew Symbols

Font Command Shorthands

All Fonts

Blackboard Bold `\mathbb{}`

Bold `\mathbf{}`

Bold Greek Letters `\boldsymbol{}`

Italic (Default for Latin Letters)`\mathit{}`

Italic Greek Letters (Default for Lowercase Letters)`\mathit{}`

Roman `\mathrm{}`

Sans Serif `\mathsf{}`

Sans Serif Greek Letters (Uppercase Only)`\mathsf{}`

Script / Calligraphic `\mathcal{}`

Fraktur `\mathfrak{}`

Lowercase Script `\mathscr{}`

Mixed Fonts

Explanatory Text

Delimiters

Spacing

Colors Supported by Older Browsers

Custom RGB Colors

Supported Color Palette

Examples