MathJax - Tex : Quick Reference Guide

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More efficient than a long tutorial, MathJax / Tex equations examples.

Block mode"Inline" mode
Equation code writing $$ Tex code $$ \[ Tex code \] $ Tex code $ ## Tex code ## \( Tex code \)

Matrices

$$ \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ \end{pmatrix} $$
$$
   \begin{pmatrix}
     1 & 2 \\
     3 & 4 \\
   \end{pmatrix}
$$
$$ \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ \end{bmatrix} $$
$$
   \begin{bmatrix}
     1 & 2 \\
     3 & 4 \\
   \end{bmatrix}
$$
$$ \begin{Bmatrix} 1 & 2 \\ 3 & 4 \\ \end{Bmatrix} $$
$$
   \begin{Bmatrix}
     1 & 2 \\
     3 & 4 \\
   \end{Bmatrix}
$$
$$ \begin{vmatrix} 1 & 2 \\ 3 & 4 \\ \end{vmatrix} $$
$$
   \begin{vmatrix}
     1 & 2 \\
     3 & 4 \\
   \end{vmatrix}
$$
$$ \begin{Vmatrix} 1 & 2 \\ 3 & 4 \\ \end{Vmatrix} $$
$$
   \begin{Vmatrix}
     1 & 2 \\
     3 & 4 \\
   \end{Vmatrix}
$$

To omit entries :

$$ \begin{pmatrix} 1 & a_1 & \cdots & a_n \\ 1 & b_1 & \cdots & b_n \\ \vdots & \vdots & \ddots & \vdots \\ 1 & z_1 & \cdots & z_n \\ \end{pmatrix} $$
$$
   \begin{pmatrix}
     1      & a_1    & \cdots & a_n    \\
     1      & b_1    & \cdots & b_n    \\
     \vdots & \vdots & \ddots & \vdots \\
     1      & z_1    & \cdots & z_n    \\
   \end{pmatrix}
$$

To insert an horizontal separator : \hline

$$ \begin{vmatrix} 1 & 2 \\ \hline 3 & 4 \\ \end{vmatrix} $$
$$
   \begin{vmatrix}
     1 & 2 \\
   \hline
     3 & 4 \\
   \end{vmatrix}
$$

To insert a vertical separator : arrays

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

Inline matrices (smallmatrix) :

In matrice ##\bigl(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\bigr)##, no numbers.
In matrice
$\bigl(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\bigr)$
, no numbers.

Fractions

dfrac (displaystyle) - Fractions that do not adjust to the line but to the overall style (opening, closing elements, etc.) :

$$ \begin{pmatrix} \dfrac{1}{2} & 0 \\ 0 & \dfrac{1}{2} \\ \end{pmatrix} $$
$$
  \begin{pmatrix}
    \dfrac{1}{2} & 0            \\
    0            & \dfrac{1}{2} \\
  \end{pmatrix}
$$

cfrac - Continuous fractions :

$$ x = \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+\dotsb} } } $$
$$
x = \cfrac{1}{\sqrt{2}+
      \cfrac{1}{\sqrt{2}+
        \cfrac{1}{\sqrt{2}+\dotsb}
      }
    }
$$

Definitions by cases (piecewise functions)

$$ f(n) = \begin{cases} \dfrac{n+1}{2} &, \text{if $n$ is even} \\ \\ \dfrac{n}{2} &, \text{if $n$ is odd} \end{cases} \text{for all n} \in \mathbb N $$
$$  f(n) =
\begin{cases}
  \dfrac{n+1}{2} &, \text{if $n$ is even} \\ \\
  \dfrac{n}{2}   &, \text{if $n$ is odd}
\end{cases}
\text{for all n} \in \mathbb N     
$$

Arrays

$$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 1 & 1 & 1 \\ 2 & 10 & 100 & 10 \\ 3 & 100 & 1000 & 100 \end{array} $$
$$
\begin{array}{c|lcr}
  n & \text{Left} & \text{Center} & \text{Right} \\
  \hline
  1   & 1      & 1     & 1     \\
  2   & 10     & 100   & 10    \\
  3   & 100    & 1000  & 100
\end{array}
$$

Centering equations on the sign =

$$ \begin{align} f(x) &= \frac{x+1}{x-2} \\ f'(x) &= \frac{(x-2) - (x+1)}{(x-2)^2} \\ &= - \frac{3}{x^2 - 4x + 4} \end{align} $$
$$
\begin{align}
  f(x)   &= \frac{x+1}{x-2} \\
  f'(x)  &= \frac{(x-2) - (x+1)}{(x-2)^2} \\
         &= - \frac{3}{x^2 - 4x + 4}
\end{align}
$$

Equations systems :

$$ \left \{ \begin{align} 2x + y − 2z &= 3 \\ x − y − z &= 0 \\ x + y + 3z &= 12 \end{align} \right. $$
$$
\left \{
  \begin{align}
     2x	+	y	−	2z  &=	3   \\
     x	−	y	−	z    &=	0   \\
     x	+	y	+	3z   &=	12
  \end{align}  
\right.
$$

Numbering equations (tag)

$$ \begin{align} \cos 2\theta &= \cos^2 \theta - \sin^2 \theta \tag{2} \\ 1 &= \cos^2 \theta + \sin^2 \theta \tag{3} \\ \end{align} $$
$$
\begin{align}
  \cos 2\theta  &= \cos^2 \theta - \sin^2 \theta  \tag{2}   \\ 

  1             &= \cos^2 \theta + \sin^2 \theta  \tag{3}   \\
\end{align}
$$

Tags and references (label, ref)

$$ \begin{align} \cos 2x &= \cos^2x - \sin^2x \tag{4} \label{cos2x} \\ 1 &= \cos^2x + \sin^2x \tag{5} \label{5} \\ \end{align} $$ We deduce from the formulas \( \ref{cos2x} \) and \( \ref{5} \) : $$ \begin{align} \cos 2x &= \cos^2x + \sin^2x - \sin^2x - \sin^2x \\ \\ &= 1 - 2\sin^2x \end{align} $$
$$
\begin{align}
  \cos 2x  &= \cos^2x - \sin^2x  \tag{4} \label{cos2x} \\ 

  1        &= \cos^2x + \sin^2x  \tag{5} \label{5}     \\
\end{align}
$$
We deduce from the formulas $\ref{cos2x}$ and $\ref{5}$ :
$$
\begin{align}
  \cos 2x &= \cos^2x + \sin^2x - \sin^2x - \sin^2x     \\ \\
          &= 1 - 2\sin^2x
\end{align}  
$$

Highlighting equations (bbox)

$$ \bbox[8px,border:2px solid red] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n } $$
$$ \bbox[8px,border:2px solid red]
{
   e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
}
$$
$$ \bbox[#FFA,8px,border:2px solid red] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n } $$
$$ \bbox[#FFA,8px,border:2px solid red]
{
   e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
}
$$

CSS styles (class)

The syntax \bbox to apply a style implies hard coded properties. Using the syntax \class, a stylesheet can be applied, easier for maintenance :

$$ \class{cmjx-highlight} { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n } $$
$$ \class{cmjx-highlight}
{
   e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
}
$$
.cmjx-highlight { border: 2px solid #DD4A68;
                  padding: 8px; margin-right: 4px; }

Another example which does not deal with highlighting equations :

$$ ax^2 + bx + c = 0 \\ x = \frac{-b \pm \sqrt{\Delta}}{2a} \class{cmjx-note} { \text{rem : } \Delta=b^2-4ac > 0 } $$
$$
    ax^2 + bx + c = 0 \\

    x = \frac{-b \pm \sqrt{\Delta}}{2a}
    \class{cmjx-note} { \text{rem : } \Delta=b^2-4ac > 0 }
$$
.cmjx-note {
  transform: translate(100px);
  font-size: 0.8em;
  color: #DD4A68;
}

displaystyle, textstyle

Integral ##\int_{a}^{b} x^2 \,dx## inside text
Integral $ int_{a}^{b} x^2 \,dx $ inside text
Integral ##\displaystyle{ \int_{a}^{b} x^2 \,dx }## inside text using \displaystyle
Integral $ \displaystyle{ int_{a}^{b} x^2 \,dx } $ inside text
using \displaystyle
A sum inside block : $$ \sum_{n=1}^\infty \frac{1}{n^2} $$
$$ \sum_{n=1}^\infty \frac{1}{n^2} $$
A sum inside block in text mode using \textstyle : $$ \textstyle{ \sum_{n=1}^\infty \frac{1}{n^2} } $$
$$ \textstyle{ \sum_{n=1}^\infty \frac{1}{n^2} } $$