What is LaTeX

LaTeX is a markup language that can beautifully output documents containing complex structures such as mathematical expressions, and is often used in scientific fields such as mathematics and physics. Mathematical expressions can be represented in LaTeX text by inserting a string between the symbols $ and $.

Mathematical expressions in LaTeX

Mathematical expression	LaTeX
$\equiv$	$\equiv$
$\approx$	$\approx$
$\fallingdotseq$	$\fallingdotseq$
$\risingdotseq$	$\risingdotseq$
$\sim$	`$\simeq`
$\geq$	`$\geq`
$\geqq$	`$\geqq`
$\leq$	`$\leq`
$\leqq$	`$\leqq`
$\gg$	`$\gg`
$\ll$	`$\ll`
$\N$	`$\N`
$\Z$	`$\Z`
$\R$	`$\R`
$\exist$	`$\exist`
$\forall$	`$\forall`
$\times$	`$\times`
$\ast$	`$\ast`
$\div$	`$\div`
$\pm$	`$\pm`
$\mp$	`$\mp`
$\oplus$	`$\oplus`
$\ominus$	`$\ominus`
$\otimes$	`$\otimes`
$\oslash$	`$\oslash`
$\circ$	`$\circ`
$\ltimes$	`$\ltimes`
$\rtimes$	`$\rtimes`
$\in$	`$\in`
$\ni$	`$\ni`
$\notin$	`$\notin`
$\subset$	`$\subset`
$\supset$	`$\supset`
$\subseteq$	`$\subseteq`
$\supseteq$	`$\supseteq`
$\nsubseteq$	`$\nsubseteq`
$\nsupseteq$	`$\nsupseteq`
$\cap$	`$\cap`
$\cup$	`$\cup`
$\emptyset$	`$\emptyset`
$\varnothing$	`$\varnothing`
$\parallel$	`$\parallel`
$x^2$	$x^2$
$x^{10}$	$x^{10}$
$x^{y+1}$	$x^{y+1}$
$x_i$	$x_i$
$x_i^2$	$x_i^2$
$_n C _r$	$_n C _r$
$\mathrm{e}^x$	$\mathrm{e}^x$
$\pi$	$\pi$
$\alpha$	$\alpha$
$\beta$	$\beta$
$\gamma$	$\gamma$
$\mu$	$\mu$
$\nu$	$\nu$
$\theta$	$\theta$
$\eta$	$\eta$
$\delta$	$\delta$
$\zeta$	$\zeta$
$\ell$	$\ell$
$\epsilon$	$\epsilon$
$\sigma$	$\sigma$
$\lambda$	$\lambda$
$\tau$	$\tau$
$\omega$	$\omega$
$\phi$	$\phi$
$\chi$	$\chi$
$\nabla$	$\nabla$
$\psi$	$\psi$
$\kappa$	$\kappa$
$\xi$	$\xi$
$\varepsilon$	$\varepsilon$
$\vartheta$	$\vartheta$
$\varpi$	$\varpi$
$\varsigma$	$\varsigma$
$\varphi$	$\varphi$
$\Gamma$	$\Gamma$
$\Delta$	$\Delta$
$\Omega$	$\Omega$
$\to$	$\to$
$\rightarrow$	$\rightarrow$
$\Rightarrow$	$\Rightarrow$
$\leftarrow$	$\leftarrow$
$\Leftarrow$	$\Leftarrow$
$\leftrightarrow$	$\leftrightarrow$
$\Leftrightarrow$	$\Leftrightarrow$
$\models$	$\models$
$\cdots$	$\cdots$
$\sin(x)$	$\sin(x)$
$\cos(x)$	$\cos(x)$
$\tan(x)$	$\tan(x)$
$\neq$	$\neq$
$x_1, x_2, \cdots, x_n$	$x_1, x_2, \cdots, x_n$
$\dot{x}$	$\dot{x}$
$\ddot{x}$	$\ddot{x}$
$\vec{x}$	$\vec{x}$
$\hat{x}$	$\hat{x}$
$\bar{x}$	$\bar{x}$
$\tilde{x}$	$\tilde{x}$
$\overrightarrow{x}$	$\overrightarrow{x}$
$\overleftarrow{x}$	$\overleftarrow{x}$
$\infty$	$\infty$
$\int$	$\int$
$\lim$	$\lim$
$\lim_{n\to \infty} a_n$	$\lim_{n\to \infty} a_n$
$\mathrm{d} x$	$\mathrm{d} x$
$F(x)=\int f(x) \mathrm{d} x$	$F(x) = \int f(x) \mathrm{d} x$
$\sqrt{x}$	$\sqrt{x}$
$\sqrt[n]{a}$	$\sqrt[n]{a}$
$\int_{-\infty}^{\infty} \mathrm{e}^{-x^2} \mathrm{d} x$	$\int_{-\infty}^{\infty} \mathrm{e}^{-x^2} \mathrm{d} x$
$\sum$	$\sum$
$\sum_i^N x_i$	$\sum_i^N x_i$
$\prod$	$\prod$
$\prod_i x_i$	$\prod_i x_i$
$\frac{1}{2}$	$\frac{1}{2}$
$\sum_{k=0}^\infty \frac{h^k f^{k}(x)}{k!}$	$\sum_{k=0}^\infty \frac{h^k f^{k}(x)}{k!}$
$a \mathrm{a}$	$a \mathrm{a}$
$\left( \right)$	$\left \right)$
$\left( \frac{x}{y} \right)$	$\left( \frac{x}{y} \right)$
$\left[ \frac{x}{y} \right]$	$\left[ \frac{x}{y} \right]$
$\left( \frac{x}{y} \right.$	$\left( \frac{x}{y} \right.$
$\partial$	$\partial$
$\frac{\partial f}{\partial x}$	$\frac{\partial f}{\partial x}$
$\\$	$\\$
$\quad$	$\quad$
$\underset{k}{\textrm{argmax}}$	$\underset{k}{\textrm{argmax}}$
$\textrm{precision} × \textrm{recall}$	$\textrm{precision} × \textrm{recall}$

Differential

\left. \frac{dy}{dx} \right|_{x=1}

$$
\left. \frac{dy}{dx} \right|_{x=1}
$$

Multiline Equation

\begin{aligned} (x+y)^2 &= (x+y) (x+y) \\ &= x(x+y) + y (x+y) \\ &= x^2 + xy + yx + y^2 \\ &= x^2 + 2xy+y^2 \end{aligned}

$$
\begin{aligned}
  (x+y)^2 &= (x+y) (x+y) \\
  &= x(x+y) + y (x+y) \\
  &= x^2 + xy + yx + y^2 \\
  &= x^2 + 2xy+y^2
\end{aligned}
$$

Matrix

\begin{pmatrix} a & b\\ c & d \end{pmatrix}

$$
\begin{pmatrix}
  a & b\\
  c & d
\end{pmatrix}
$$

\begin{bmatrix} a & b\\ c & d \end{bmatrix}

\begin{bmatrix}
a & b\\
c & d
\end{bmatrix}

\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}

$$
\begin{Vmatrix}
  a & b \\
  c & d
\end{Vmatrix}
$$

\left( \begin{array}{c} (x^{1})^T\\ \vdots\\ (x^{N})^T\\ \end{array} \right)

$$
\left(
  \begin{array}{c}
    (x^{1})^T\\
    \vdots\\
    (x^{N})^T\\
  \end{array}
\right)
$$

A = \left( \begin{array}{ccccc} 1 & 1 & 4 & 5 & 1 \\ 1 & 0 & 5 & 0 & 4 \\ 4 & 5 & 1 & 4 & 0 \end{array} \right)

$$
A = \left(
  \begin{array}{ccccc}
    1 & 1 & 4 & 5 & 1 \\
    1 & 0 & 5 & 0 & 4 \\
    4 & 5 & 1 & 4 & 0
  \end{array}
\right)
$$

\begin{pmatrix} a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\ \vdots & \ddots & & & \vdots \\ a_{i1} & & a_{ii} & & a_{in} \\ \vdots & & & \ddots & \vdots \\ a_{n1} & \cdots & a_{ni} & \cdots & a_{nn} \end{pmatrix} \times \begin{vmatrix} a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\ \vdots & \ddots & & & \vdots \\ a_{i1} & & a_{ii} & & a_{in} \\ \vdots & & & \ddots & \vdots \\ a_{n1} & \cdots & a_{ni} & \cdots & a_{nn} \end{vmatrix}

$$
\begin{pmatrix}
  a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\
  \vdots & \ddots &        &        & \vdots \\
  a_{i1} &        & a_{ii} &        & a_{in} \\
  \vdots &        &        & \ddots & \vdots \\
  a_{n1} & \cdots & a_{ni} & \cdots & a_{nn}
\end{pmatrix}

\times

\begin{vmatrix}
  a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\
  \vdots & \ddots &        &        & \vdots \\
  a_{i1} &        & a_{ii} &        & a_{in} \\
  \vdots &        &        & \ddots & \vdots \\
  a_{n1} & \cdots & a_{ni} & \cdots & a_{nn}
\end{vmatrix}
$$

Conditional Branch

f(x) = \left\{ \begin{array}{ll} 1 & (x = 1) \\ 0 & (otherwise) \end{array} \right.

$$
f(x) = \left\{
  \begin{array}{ll}
    1 & (x = 1) \\
    0 & (otherwise)
  \end{array}
\right.
$$

Equation Number

\tag{1.0.2} x_i = \sigma (W_i + \beta)

$$
\tag{1.0.2}
x_i = \sigma (W_i + \beta)
$$

Linear Programming

\begin{equation*} \begin{aligned} & \text{minimize} & {\bf c}^T{\bf x} \\ & \text{s.t.} & A{\bf x} \le {\bf b} \\ & & {\bf x} \ge {\bf 0} \\ \end{aligned} \end{equation*}

$$
\begin{equation*}
  \begin{aligned}
    & \text{minimize}
      & {\bf c}^T{\bf x} \\
    & \text{s.t.}
      & A{\bf x} \le {\bf b} \\
      & & {\bf x} \ge {\bf 0} \\
  \end{aligned}
\end{equation*}
$$

Simplex Method

\begin{array}{rrrrrrr} x_3 & = & 1 & + & x_1 & - & x_2 \\ x_4 & = & 3 & - & x_1 & & \\ x_5 & = & 2 & & & - & x_2 \\ \hline z & = & & & x_1 & + & x_2 \end{array}

$$
\begin{array}{rrrrrrr}
  x_3 & = & 1 & + & x_1 & - & x_2 \\
  x_4 & = & 3 & - & x_1 &   &     \\
  x_5 & = & 2 &   &     & - & x_2 \\ \hline
  z   & = &   &   & x_1 & + & x_2
\end{array}
$$

Mathematical expression in LaTeX