\section{Environments}
Matrix environments
amsmath provides six matrix environments, each producing a different bracket style. All use the same row/column syntax — only the surrounding delimiters change.
Bare matrix with no surrounding brackets. Wrap manually in \left( ... \right) if needed.
Matrix enclosed in parentheses. The most common form for linear algebra.
Matrix enclosed in square brackets. Common in engineering and control theory.
Matrix enclosed in curly braces. Occasionally used for set-builder notation.
Matrix enclosed in single vertical bars. Standard notation for determinants.
Matrix enclosed in double vertical bars. Used for matrix norms.
\begin{pmatrix}
Syntax walkthrough
The matrix syntax mirrors the tabular environment: columns are separated by & and rows end with \\. Unlike tables, you do not specify column alignment — matrix columns are always centered.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
% No delimiters
\[
\begin{matrix}
1 & 0 \\ 0 & 1
\end{matrix}
\]
% Parentheses — pmatrix
\[
A = \begin{pmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{pmatrix}
\]
% Square brackets — bmatrix
\[
B = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}
\]
% Vertical bars (determinant) — vmatrix
\[
\det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc
\]
\end{document}&
Column separator
Separates entries within a row, just like in tabular.
\\
Row separator
Ends the current row and starts a new one.
a_{ij}
Subscript notation
Standard index notation for the (i, j) entry.
\begin{array}
Augmented matrices with array
amsmath matrix environments do not support a vertical dividing line. For augmented matrices (e.g., for row-reduction), use the built-in array environment inside manual \left[...\right] delimiters. Add a | in the column spec to draw the vertical separator.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
% Augmented matrix — use array with a vertical rule
\[
\left[\begin{array}{ccc|c}
1 & 2 & 3 & 4 \\
0 & 1 & 2 & 3 \\
0 & 0 & 1 & 2
\end{array}\right]
\]
% 3x3 identity matrix
\[
I_3 = \begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}
\]
\end{document}\section{Try it live}
3 × 3 matrix example
Open this complete 3×3 matrix example — including a pmatrix and a vmatrix determinant — directly in the FormaTeX playground and compile it with one click.
\section{Common mistakes}
Avoid these pitfalls
Using matrix environments outside math mode
All amsmath matrix environments must be inside \[...\] or another math environment. Placing \begin{pmatrix} directly in the document body will cause a compilation error.
Inconsistent column counts
Every row must have the same number of & separators. A 3-column matrix needs exactly two & per row. Inconsistent counts produce misaligned output or errors.
Trying to add a vertical line inside pmatrix
pmatrix and its siblings do not accept a column spec, so you cannot insert a | divider. Use the array environment inside \left[...\right] for augmented matrices instead.
\section{FAQ}
Frequently asked questions
What package do I need for LaTeX matrix environments?
All matrix environments (matrix, pmatrix, bmatrix, vmatrix, etc.) are provided by the amsmath package. Add \usepackage{amsmath} to your preamble. The array environment for augmented matrices is built into LaTeX and does not need any extra package.
How do I write a determinant in LaTeX?
Use the vmatrix environment from amsmath: \begin{vmatrix} a & b \\ c & d \end{vmatrix}. This places the matrix between single vertical bars. For a 2×2 determinant the result is |A| = ad - bc.
How do I create an augmented matrix in LaTeX?
Use the array environment with a column spec that includes a vertical bar. For example: \left[\begin{array}{cc|c} a & b & e \\ c & d & f \end{array}\right]. The | in the column spec {cc|c} draws the vertical line separating the coefficient and constant columns.
How many columns can a LaTeX matrix have?
There is no hard limit on matrix columns in standard LaTeX. However, very wide matrices may overflow the text area. For matrices wider than the page, consider using \resizebox from the graphicx package, or splitting the matrix across multiple equations.
How do I add dots (ellipsis) inside a matrix?
Use \cdots for horizontal dots, \vdots for vertical dots, and \ddots for diagonal dots. For example: \begin{pmatrix} 1 & \cdots & n \\ \vdots & \ddots & \vdots \\ n & \cdots & n^2 \end{pmatrix}
\section{Related guides}