LaTeX Matrices
Six environments for six bracket styles. & separates columns, \\ separates rows. Always inside math mode.
The basic pattern
\usepackage{amsmath}
% 2x2 matrix with parentheses
$\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}$
% 3x3 with square brackets
$\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}$
% Determinant
$\begin{vmatrix}
a & b \\
c & d
\end{vmatrix} = ad - bc$The seven matrix environments
| Environment | Brackets / use |
|---|---|
| matrix | No brackets — bare matrix |
| pmatrix | ( ) parentheses |
| bmatrix | [ ] square brackets |
| Bmatrix | { } curly braces |
| vmatrix | | | single bars (determinant) |
| Vmatrix | ‖ ‖ double bars (norm) |
| smallmatrix | Inline-sized matrix for cramped spaces |
Column vector and row vector
% Column vector
$\mathbf{v} = \begin{pmatrix} x \\ y \\ z \end{pmatrix}$
% Row vector
$\mathbf{v}^T = \begin{pmatrix} x & y & z \end{pmatrix}$Matrix with ellipsis (general n×n)
$A = \begin{pmatrix}
a_{11} & a_{12} & \dots & a_{1n} \\
a_{21} & a_{22} & \dots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \dots & a_{mn}
\end{pmatrix}$Right-aligned matrix entries
% Right-align — useful when entries have negative signs
$\begin{pmatrix*}[r]
-1 & 2 \\
3 & -4
\end{pmatrix*}$Inline small matrix
The matrix $\bigl(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\bigr)$
fits inline without breaking the line height.Common mistakes
- Forgetting
\usepackage{amsmath}. All matrix environments need it. - Inconsistent column count. Each row needs the same number of
&separators. - Missing math mode. Wrap in
$ ... $or use a display environment. - Trailing
\\on the last row. Sometimes causes errors — try removing it if you get a complaint.
$ mat(a, b; c, d) $ // square brackets default
$ mat(delim: "(", a, b; c, d) $ // parens
$ mat(delim: "|", a, b; c, d) $ // determinantOne mat() function with a delimiter argument. Try TypeTeX free.
Frequently Asked Questions
Use the pmatrix environment from amsmath: \begin{pmatrix} a & b \\ c & d \end{pmatrix} produces a 2x2 matrix in parentheses. Columns are separated by &, rows by \\. Always inside math mode ($ ... $ or display).
Just the brackets: pmatrix uses parentheses (), bmatrix uses square brackets [], Bmatrix uses curly braces {}, vmatrix uses single vertical bars | | (used for determinants), Vmatrix uses double vertical bars ‖ ‖ (used for norms). The contents and syntax are identical.
Use vmatrix: \begin{vmatrix} a & b \\ c & d \end{vmatrix} renders as |a b; c d| with single vertical bars indicating the determinant. Or write it as \det\begin{pmatrix} a & b \\ c & d \end{pmatrix} for an explicit 'det' label.
Use pmatrix or bmatrix with one column: \begin{pmatrix} x \\ y \\ z \end{pmatrix}. Rows are separated by \\. For a row vector, write it as a 1xN matrix: \begin{pmatrix} x & y & z \end{pmatrix}.
Use matrix* (or pmatrix*, bmatrix*, etc.) with a column-alignment argument: \begin{pmatrix*}[r] -1 & 2 \\ 3 & -4 \end{pmatrix*} right-aligns negative numbers cleanly. Use [l] for left, [c] for center (default).
\dots for horizontal, \vdots for vertical (top to bottom), \ddots for diagonal (top-left to bottom-right). Common in theory papers: \begin{pmatrix} a_{11} & \dots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{m1} & \dots & a_{mn} \end{pmatrix}.
Use \begin{pmatrix*}[c|c] for vertical partition with a separator. The pipe character | adds a vertical line. For more flexibility, use \begin{array}{c|c c} ... \end{array} wrapped in \left( ... \right). The blkarray package handles complex block layouts.
Use smallmatrix: $\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$. The \bigl( \bigr) provides the parentheses since smallmatrix doesn't include them. Useful when matrices appear inline in body text.
Three common causes: (1) missing \usepackage{amsmath}; (2) using a literal | for vmatrix instead of the environment; (3) inconsistent column counts (one row has more & than another). Check the column count is uniform across all rows.
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