Brackets, Matrices, and Arrays

Brackets

Scale brackets automatically using \left and \right.

Parentheses ( )

$$ \left( \frac{1}{2} \right) $$ \left( ... \right)

Square Brackets [ ]

$$ \left[ \begin{matrix} 1 & 0 \ 0 & 1 \end{matrix} \right] $$ \left[ ... \right]

Curly Braces { }

$$ \left{ x \in \mathbb{R} \mid x > 0 \right} $$ \left\{ ... \right\} (Must escape \{!)

Absolute Value | |

$$ \left| -5 \right| = 5 $$ \left| ... \right|

Angle Brackets < >

$$ \langle u, v \rangle $$ \langle ... \rangle or \left\langle ... \right\rangle

Matrices and Arrays

Requires amsmath. Standard environments:

• matrix: No brackets.
• pmatrix: Parentheses ( ).
• bmatrix: Square brackets [ ].
• Bmatrix: Curly braces { }.
• vmatrix: Single bars | | (determinant).
• Vmatrix: Double bars || || (norm).

The structure is similar to a table:

• Rows are separated by \\.
• Columns are separated by &.

Examples

pmatrix: $$ \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} $$

\begin{pmatrix}
  1 & 2 \\
  3 & 4
\end{pmatrix}

bmatrix: $$ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} $$

\begin{bmatrix}
  1 & 2 & 3 \\
  4 & 5 & 6 \\
  7 & 8 & 9
\end{bmatrix}

Creating Cases Functions

Use the cases environment for piecewise functions.

\[ f(x) = \begin{cases} 2x & x > 0 \\ 0 & x \le 0 \end{cases} \]

f(x) = \begin{cases}
  2x & x > 0 \\
  0 & x \le 0
\end{cases}