Matrices
========


1. Use `$$\begin{matrix}…\end{matrix}$$` In between the `\begin` and `\end`, put the matrix elements. End each matrix row with `\\`, and separate matrix elements with `&`. For example,

 $$
 \begin{matrix}
 1 & x & x^2 \\
 1 & y & y^2 \\
 1 & z & z^2 \\
 \end{matrix}
$$

 produces:

 $$
 \begin{matrix}
 1 & x & x^2 \\
 1 & y & y^2 \\
 1 & z & z^2 \\
 \end{matrix}
$$

 MathJax will adjust the sizes of the rows and columns so that everything fits. 

2. To add brackets, either use `\left…\right` as in section 6 of the tutorial, or replace `matrix` with `pmatrix` $\begin{pmatrix}1&2\\3&4\\ \end{pmatrix}$, `bmatrix` $\begin{bmatrix}1&2\\3&4\\ \end{bmatrix}$, `Bmatrix` $\begin{Bmatrix}1&2\\3&4\\ \end{Bmatrix}$, `vmatrix` $\begin{vmatrix}1&2\\3&4\\ \end{vmatrix}$, `Vmatrix` $\begin{Vmatrix}1&2\\3&4\\ \end{Vmatrix}$.

3. Use `\cdots` $\cdots$ `\ddots` $\ddots$ `\vdots` $\vdots$ when you want to omit some of the entries:

 $$\begin{pmatrix}
 1 & a_1 & a_1^2 & \cdots & a_1^n \\
 1 & a_2 & a_2^2 & \cdots & a_2^n \\
 \vdots & \vdots& \vdots & \ddots & \vdots \\
 1 & a_m & a_m^2 & \cdots & a_m^n 
 \end{pmatrix}$$ 


4. For horizontally "augmented" matrices, put parentheses or brackets around a suitably-formatted table; see [arrays](http://meta.math.stackexchange.com/a/5044/) below for details. Here is an example:

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

 is produced by:

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

 The `cc|c` is the crucial part here; it says that there are three centered columns with a vertical bar between the second and third.

5. For vertically "augmented" matrices, use `\hline`. For example

$$
\begin{pmatrix}
a & b \\
c & d\\
\hline
1 & 0\\
0 & 1
\end{pmatrix}
$$
is produced by

 $$
 \begin{pmatrix}
 a & b\\
 c & d\\
 \hline
 1 & 0\\
 0 & 1
 \end{pmatrix}
 $$


6. For small inline matrices use `\bigl(\begin{smallmatrix} ... \end{smallmatrix}\bigr)`, e.g. $\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$ is produced by:
 
 $\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$