Latex math symbols

Machine Learning 2009. 3. 11. 11:38

Operators

Symbol	Command	Symbol	Command	Symbol	Command
$\pm$	\pm	$\mp$	\mp	$\times$	\times
$\div$	\div	$\cdot$	\cdot	$\ast$	\ast
$\star$	\star	$\dagger$	\dagger	$\ddagger$	\ddagger
$\amalg$	\amalg	$\cap$	\cap	$\cup$	\cup
$\uplus$	\uplus	$\sqcap$	\sqcap	$\sqcup$	\sqcup
$\vee$	\vee	$\wedge$	\wedge	$\oplus$	\oplus
$\ominus$	\ominus	$\otimes$	\otimes	$\circ$	\circ
$\bullet$	\bullet	$\diamond$	\diamond	$\lhd$	\lhd
$\rhd$	\rhd	$\unlhd$	\unlhd	$\unrhd$	\unrhd
$\oslash$	\oslash	$\odot$	\odot	$\bigcirc$	\bigcirc
$\triangleleft$	\triangleleft	$\Diamond$	\Diamond	$\bigtriangleup$	\bigtriangleup
$\bigtriangledown$	\bigtriangledown	$\Box$	\Box	$\triangleright$	\triangleright
$\setminus$	\setminus	$\wr$	\wr

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Relations

Symbol	Command	Symbol	Command	Symbol	Command
$\le$	\le	$\ge$	\ge	$\neq$	\neq
$\sim$	\sim	$\ll$	\ll	$\gg$	\gg
$\doteq$	\doteq	$\simeq$	\simeq	$\subset$	\subset
$\supset$	\supset	$\approx$	\approx	$\asymp$	\asymp
$\subseteq$	\subseteq	$\supseteq$	\supseteq	$\cong$	\cong
$\smile$	\smile	$\sqsubset$	\sqsubset	$\sqsupset$	\sqsupset
$\equiv$	\equiv	$\frown$	\frown	$\sqsubseteq$	\sqsubseteq
$\sqsupseteq$	\sqsupseteq	$\propto$	\propto	$\bowtie$	\bowtie
$\in$	\in	$\ni$	\ni	$\prec$	\prec
$\succ$	\succ	$\vdash$	\vdash	$\dashv$	\dashv
$\preceq$	\preceq	$\succeq$	\succeq	$\models$	\models
$\perp$	\perp	$\parallel$	\parallel	$\\|$	\\|
$\mid$	\mid

Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an n between the \ and the word. Here are a few examples, plus a few other negations; it works for many of the others as well.

Symbol	Command	Symbol	Command	Symbol	Command
$\nmid$	\nmid	$\nleq$	\nleq	$\ngeq$	\ngeq
$\nsim$	\nsim	$\ncong$	\ncong	$\nparallel$	\nparallel
$\not<$	\not<	$\not>$	\not>	$\not=$	\not=
$\not\le$	\not\le	$\not\ge$	\not\ge	$\not\sim$	\not\sim
$\not\approx$	\not\approx	$\not\cong$	\not\cong	$\not\equiv$	\not\equiv
$\not\parallel$	\not\parallel	$\nless$	\nless	$\ngtr$	\ngtr
$\lneq$	\lneq	$\gneq$	\gneq	$\lnsim$	\lnsim
$\lneqq$	\lneqq	$\gneqq$	\gneqq

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Greek Letters

Lowercase letters

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

Capital letters

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

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Arrows

Symbol	Command	Symbol	Command
$\gets$	\gets	$\to$	\to
$\leftarrow$	\leftarrow	$\Leftarrow$	\Leftarrow
$\rightarrow$	\rightarrow	$\Rightarrow$	\Rightarrow
$\leftrightarrow$	\leftrightarrow	$\Leftrightarrow$	\Leftrightarrow
$\mapsto$	\mapsto	$\hookleftarrow$	\hookleftarrow
$\leftharpoonup$	\leftharpoonup	$\leftharpoondown$	\leftharpoondown
$\rightleftharpoons$	\rightleftharpoons	$\longleftarrow$	\longleftarrow
$\Longleftarrow$	\Longleftarrow	$\longrightarrow$	\longrightarrow
$\Longrightarrow$	\Longrightarrow	$\longleftrightarrow$	\longleftrightarrow
$\Longleftrightarrow$	\Longleftrightarrow	$\longmapsto$	\longmapsto
$\hookrightarrow$	\hookrightarrow	$\rightharpoonup$	\rightharpoonup
$\rightharpoondown$	\rightharpoondown	$\leadsto$	\leadsto
$\uparrow$	\uparrow	$\Uparrow$	\Uparrow
$\downarrow$	\downarrow	$\Downarrow$	\Downarrow
$\updownarrow$	\updownarrow	$\Updownarrow$	\Updownarrow
$\nearrow$	\nearrow	$\searrow$	\searrow
$\swarrow$	\swarrow	$\nwarrow$	\nwarrow

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Dots

Symbol	Command	Symbol	Command	Symbol	Command	Symbol	Command
$\ldots 2$	\ldots 2	$\vdots$	\vdots	$\cdots 2$	\cdots 2	$\ddots$	\ddots

(The '2's after \ldots and \cdots are only present to make the distinction between the two clear.)

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Accents

Symbol	Command	Symbol	Command	Symbol	Command
$\hat{x}$	\hat{x}	$\check{x}$	\check{x}	$\dot{x}$	\dot{x}
$\breve{x}$	\breve{x}	$\acute{x}$	\acute{x}	$\ddot{x}$	\ddot{x}
$\grave{x}$	\grave{x}	$\tilde{x}$	\tilde{x}	$\mathring{x}$	\mathring{x}
$\bar{x}$	\bar{x}	$\vec{x}$	\vec{x}

When applying accents to i and j, you can use \imath and \jmath to keep the dots from interfering with the accents:

Symbol	Command	Symbol	Command
$\vec{\jmath}$	\vec{\jmath}	$\tilde{\imath}$	\tilde{\imath}

\tilde and \hat have wide versions that allow you to accent an expression:

Symbol	Command	Symbol	Command
$\widehat{3+x}$	\widehat{3+x}	$\widetilde{abc}$	\widetilde{abc}

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Others

Symbol	Command	Symbol	Command	Symbol	Command
$\infty$	\infty	$\triangle$	\triangle	$\angle$	\angle
$\aleph$	\aleph	$\hbar$	\hbar	$\imath$	\imath
$\jmath$	\jmath	$\ell$	\ell	$\wp$	\wp
$\Re$	\Re	$\Im$	\Im	$\mho$	\mho
$\prime$	\prime	$\emptyset$	\emptyset	$\nabla$	\nabla
$\surd$	\surd	$\partial$	\partial	$\top$	\top
$\bot$	\bot	$\vdash$	\vdash	$\dashv$	\dashv
$\forall$	\forall	$\exists$	\exists	$\neg$	\neg
$\flat$	\flat	$\natural$	\natural	$\sharp$	\sharp
$\backslash$	\backslash	$\Box$	\Box	$\Diamond$	\Diamond
$\clubsuit$	\clubsuit	$\diamondsuit$	\diamondsuit	$\heartsuit$	\heartsuit
$\spadesuit$	\spadesuit	$\Join$	\Join	$\blacksquare$	\blacksquare

Didn't find what you want? Or do you want a printable list? The Comprehensive LaTex Symbol list has just about any symbol that you could possibly want.

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Bracketing Symbols

In mathematics, sometimes we need to enclose expressions in brackets or braces or parentheses. Some of these work just as you'd imagine in LaTeX; type ( and ) for parentheses, [ and ] for brackets, and | and | for absolute value. However, other symbols have special commands:

Symbol	Command	Symbol	Command	Symbol	Command
$\{$	\{	$\}$	\}	$\\|$	\\|
$\backslash$	\backslash	$\lfloor$	\lfloor	$\rfloor$	\rfloor
$\lceil$	\lceil	$\rceil$	\rceil	$\langle$	\langle
$\rangle$	\rangle

You might notice that if you use any of these to typeset an expression that is vertically large, like

\displaystyle (1 + \frac{a}{x} )^2

the parentheses don't come out the right size:

$\displaystyle (1 + \frac{a}{x} )^2$

If we put \left and \right before the relevant parentheses, we get a prettier expression:

\displaystyle \left(1 + \frac{a}{x} \right)^2

gives

$\displaystyle \left(1 + \frac{a}{x} \right)^2$

\left and \right can also be used to resize the following symbols:

Symbol	Command	Symbol	Command	Symbol	Command
$\uparrow$	\uparrow	$\downarrow$	\downarrow	$\updownarrow$	\updownarrow
$\Uparrow$	\Uparrow	$\Downarrow$	\Downarrow	$\Updownarrow$	\Updownarrow

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Multi-Size Symbols

Some symbols render differently in regular math mode and in display mode (display mode occurs when you use \displaystyle, $$...$$, or \[...\]). Read more in the commands section of the guide about how symbols which take arguments above and below the symbols, such as a summation symbol, behave in the two modes.

In each of the following, the two images show the symbol in regular mode, then in display mode.

Symbol	Command	Symbol	Command	Symbol	Command
$\textstyle\sum$ $\displaystyle\sum$	\sum	$\textstyle\int$ $\displaystyle\int$	\int	$\textstyle\oint$ $\displaystyle\oint$	\oint
$\textstyle\prod$ $\displaystyle\prod$	\prod	$\textstyle\coprod$ $\displaystyle\coprod$	\coprod	$\textstyle\bigcap$ $\displaystyle\bigcap$	\bigcap
$\textstyle\bigcup$ $\displaystyle\bigcup$	\bigcup	$\textstyle\bigsqcup$ $\displaystyle\bigsqcup$	\bigsqcup	$\textstyle\bigvee$ $\displaystyle\bigvee$	\bigvee
$\textstyle\bigwedge$ $\displaystyle\bigwedge$	\bigwedge	$\textstyle\bigodot$ $\displaystyle\bigodot$	\bigodot	$\textstyle\bigotimes$ $\displaystyle\bigotimes$	\bigotimes
$\textstyle\bigoplus$ $\displaystyle\bigoplus$	\bigoplus	$\textstyle\biguplus$ $\displaystyle\biguplus$	\biguplus

(The two integral symbols render fine in a full LaTeX document .)

복잡한 수식

여러 줄에 이어 계속되는 식이 = 등에 의해 정렬되는 경우는 eqnarray 환경을 쓰고 행렬처럼 가로세로로 정렬하려면 array, matrix 환경을 쓴다. 이러한 환경은 스스로 displaymath 모드로 바꿈으로 $$ ... $$ 로 묶지 않음에 유의하라. AMSLaTeX에서 제공하는 수식정렬 환경으로 align, gather, case 등의 환경이 있다. 다음의 예를 참고하라.

\begin{eqnarray}
Y & = & x^2+1 \\
y & > & a-b+c-d+e-f+\\
& & g-h+k-l+m
\end{eqnarray}

$$
\left( \begin{array}{rrr}
2-x & -2 & 3 \\
-3 & x-5 & 1 \\
0 & 1 & x+2
\end{array} \right)
$$

\begin{align}
2x+3y+z &= 0 \\
3x-2y+2z &= 0
\end{align}

\begin{gather}
1\\
x+x\\
x^2+2xy+y^2\\
x^3+3x^2y+3xy^2+y^3 \\
\end{gather}

eqnarray, align, gather 환경은 자동으로 수식번호를 매겨준다 (위 그림에서는 편의상 번호를 나타내지 않았다). 수식번호가 필요치 않은 경우 eqnarray*와 같이 끝에 *를 붙인다. 위 예에서 보듯이 &는 칸을 가르는 역할을 하고, \\는 줄바꿈을 한다. \begin{array}{rrr}에서 {rrr}은 array에 세 칸(열)이 있고 각 열은 오른쪽 정렬을 함을 나타낸다. r은 오른쪽 정렬을, c는 중앙정렬, l은 왼쪽정렬을 할 때 쓰인다.

$$
\varphi(x)=\begin{cases} e^{-1/x^2} & \text{ if $x\not=0$} \\
0 & \text{ if $x=0$.} \end{cases}
$$

\begin{gather*}
\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \quad
\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \\
\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \quad
\begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} \quad
\begin{Vmatrix} 1 & 0 \\ 0 & 1 \end{Vmatrix}
\end{gather*}

case 환경에서는 수학모드이기 때문에 \text{...}을 써서 보통 로만글꼴로 조건들을 표시하였음에 유의하라. 좀더 자세한 것은 AMSLaTeX User's Guide를 보자.

Cybernetics

Latex math symbols

복잡한 수식

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