11 Matrix Environment
Matrices
Like arrays, we use matrix in math mode.
(a) Set the matrix in math mode with [latex].
(b) Type \begin{pmatrix}.
(c) Type your data, using & to separate columns and \\ to move to the next row.
(d) End the matrix with \end{pmatrix} and[/latex].
Example:
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}
\begin{pmatrix} 1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{pmatrix}
The other environments in this family are bmatrix (square brackets []), Bmatrix (curly braces {}), vmatrix (vertical lines | |), and Vmatrix (double vertical lines || ||).
Small Matrices
You can also provide small matrices to fit in-line [latex](\begin{smallmatrix} a & b \\ c & d \\ \end{smallmatrix})[/latex] with text.
[latex](\begin{smallmatrix}a & b\\c & d\\ \end{smallmatrix})[/latex]
More Examples
Let us construct more complicated matrices.
Example:
a) \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\
0 & \cdots & 0 \end{bmatrix}
- Note the use of the \vdots command to produce three vertical dots in that cell. You get horizontal dots by using \cdots and diagonal ones by using \ddots.
b) \begin{align}\begin{bmatrix} xz & xw\\ yz & yw \end{bmatrix}= \begin{bmatrix} x \\ y \end{bmatrix} \times \begin{bmatrix} z & w \end{bmatrix}\end{align}
\begin{align}\begin{bmatrix} xz & xw\\ yz & yw \end{bmatrix}=
\begin{bmatrix} x \\ y \end{bmatrix} \times
\begin{bmatrix} z & w \end{bmatrix}\end{align}
Exercises
Typeset the following equation:
\begin{align}\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix}= det \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i\\ \end{bmatrix}\end{align}
When you write a matrix whose entries are fractions, you might feel the lines are cramped. So to widen the gap between lines, use \\[6pt] instead of \\ .
Example: Using \\
[latex]A=\begin{bmatrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{2}{3} &\frac{-1}{3} &\frac{-1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{-2}{3} \end{bmatrix}[/latex]
[latex]
A=\begin{bmatrix}
\frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\
\frac{2}{3} &\frac{-1}{3} &\frac{-1}{3} \\
\frac{1}{3} & \frac{1}{3} & \frac{-2}{3}
\end{bmatrix}
[/latex]
Example: Using \\[6pt]
[latex]A=\begin{bmatrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\[6pt] \frac{2}{3} &\frac{-1}{3} &\frac{-1}{3} \\[6pt] \frac{1}{3} & \frac{1}{3} & \frac{-2}{3} \end{bmatrix}[/latex]
[latex]
A=\begin{bmatrix}
\frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\[6pt]
\frac{2}{3} &\frac{-1}{3} &\frac{-1}{3} \\[6pt]
\frac{1}{3} & \frac{1}{3} & \frac{-2}{3}
\end{bmatrix}
[/latex]
