9.4.10 Arrays

Mathematical structures such as matrices and vectors require elements to be arranged in rows and columns. Just as we can align material in rows and columns in text mode using the tabular environment (§4.6. Aligning Material in Rows and Columns), we can do the same in maths mode using the array environment. The array environment has the same format as the tabular environment, however it must be in maths mode. The column half-gaps are given by the length register \arraycolsep (analogous to \tabcolsep).

Example:

\[
\begin{array}{rrr}
0 & 1 & 19\\
-6 & 10 & 200
\end{array}
\]

Example (Adding Delimiters):

\[ \left( \begin{array}{rrr} 0 & 1 & 19\\ -6 & 10 & 200 \end{array} \right) \]

Image: as before but has large round brackets on either
side.

Adding a Vertical Rule:

A vertical rule can be added using | in the column specifier. For example:

\[ \left( \begin{array}{rr|r} 0 & 1 & 19\\ -6 & 10 & 200 \end{array} \right) \]

Image: 3 columns and 2 rows with a vertical line
between the second and third column.

Example (Cases):

This example uses an invisible delimiter:

\[ f(x) = \left\{ \begin{array}{rl} -1 & x < 0\\ 0 & x = 0\\ +1 & x > 0 \end{array} \right. \]

Image: array has large open brace on the left and
nothing on the right of it.

This can be rewritten more compactly using the amsmath cases environment:

\[
f(x) =
\begin{cases}
  -1 & x < 0\\
  0 & x = 0\\
  +1 & x > 0
\end{cases}
\]

The amsmath package provides some convenient environments to typeset matrices: pmatrix, bmatrix, Bmatrix, vmatrix and Vmatrix. These are similar to the array environment except there is no argument, and they add (respectively) $\bigl( \bigr)$ , $\bigl[ \bigr]$ , $\bigl\{ \bigr\}$ , $\bigl\lvert \bigr\rvert$ and $\bigl\lVert \bigr\rVert$ delimiters. There is also the matrix environment that doesn't have any delimiters.