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 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:

     $\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$