Complete LaTeX Matrix Tutorial for Beginners

A matrix is an arrangement of numbers, symbols, or expressions in rows and columns.

In LaTeX, writing matrices is simple once you understand their structure.

This tutorial explains step by step how to define matrices, apply different brackets, and even create special matrix types using LaTeX.

Define matrix syntax

To define a matrix, you need to create a proper environment, arrange rows and columns, and insert elements. The amsmath package must be loaded to use these environments.

\begin{matrix}
..... & .... & .... \\
..... & .... & .... \\
..... & .... & .... 
\end{matrix}

\begin{matrix} ... \end{matrix}

This environment creates the basic structure for a matrix. You can choose variations like pmatrix or bmatrix to change the surrounding brackets.

& symbol

Separates elements inside a row, helping to organize them into proper columns.

\\ command

Moves to the next row in the matrix. Every new row must end with this command.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
  \begin{matrix}
    a_{11} & a_{12} \\ 
    a_{21} & a_{22}
  \end{matrix}
\]
\end{document}

Output :

Different types of brackets

LaTeX provides several environments that add different types of brackets around matrices.

Choosing the right one depends on your mathematical notation.

pmatrix	( )
bmatrix	[ ]
Bmatrix	{ }
vmatrix	| |
Vmatrix	|| ||

Without brackets

If you only need the matrix structure without any enclosing brackets, use the simple matrix environment.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
 \begin{matrix}
     a_{11} & a_{12} & a_{13} \\ 
     a_{21} & a_{22} & a_{23} \\
     a_{31} & a_{32} & a_{33} 
 \end{matrix}
\]
\end{document}

Output :

Use parentheses

For parentheses around the matrix, replace matrix with pmatrix.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[\begin{pmatrix}
     a_{11} & a_{12} & a_{13} \\ 
     a_{21} & a_{22} & a_{23} \\
     a_{31} & a_{32} & a_{33} 
 \end{pmatrix}\]
\end{document}

Output :

Use square brackets

The bmatrix environment is used for square brackets.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[\begin{bmatrix}
     a_{11} & a_{12} & a_{13} \\ 
     a_{21} & a_{22} & a_{23} \\
     a_{31} & a_{32} & a_{33} 
 \end{bmatrix}\]
\end{document}

Output :

Use curly brackets

For curly brackets, use Bmatrix. Note that case sensitivity matters.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[\begin{Bmatrix}
     a_{11} & a_{12} & a_{13} \\ 
     a_{21} & a_{22} & a_{23} \\
     a_{31} & a_{32} & a_{33} 
 \end{Bmatrix}\]
\end{document}

Output :

Use vertical bars

For single vertical bars, apply the vmatrix environment.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[\begin{vmatrix}
     a_{11} & a_{12} & a_{13} \\ 
     a_{21} & a_{22} & a_{23} \\
     a_{31} & a_{32} & a_{33} 
 \end{vmatrix}\]
\end{document}

Output :

Use double vertical bars

For double bars, use Vmatrix. Remember the capital V.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ \begin{Vmatrix}
     a_{11} & a_{12} & a_{13} \\ 
     a_{21} & a_{22} & a_{23} \\
     a_{31} & a_{32} & a_{33} 
 \end{Vmatrix} \]
\end{document}

Output :

Define different types of matrices in LaTeX

You can define special kinds of matrices based on how their elements are arranged.

Square matrix

Rows and columns are equal in size.

\[ \begin{bmatrix}
   a_{1,1} & a_{1,2} & \cdots & a_{1,m} \\
   a_{2,1} & a_{2,2} & \cdots & a_{2,m} \\
   \vdots  & \vdots  & \ddots & \vdots  \\
   a_{m,1} & a_{m,2} & \cdots & a_{m,m} 
 \end{pmatrix} \]

Output :

Null matrix

All elements are zero.

\[ \begin{bmatrix}
   0 & 0 & 0 \\ 
   0 & 0 & 0 \\ 
   0 & 0 & 0
 \end{bmatrix} \]

Output :

Diagonal matrix

Non-zero values appear only on the diagonal.

\[ \begin{bmatrix}
    a_{1} &  & \\ 
    & \ddots & \\ 
    &  &  a_{n}
 \end{bmatrix} \]

Output :

Row matrix

All elements are arranged in a single row.

\[ \begin{pmatrix}
    a_{1} & \cdots & a_{n} 
 \end{pmatrix} \]

Output :

Column matrix

All elements are arranged in a single column.

\[ \begin{bmatrix} 
   a_{1} \\ \vdots \\ a_{n} 
\end{bmatrix} \]

Output :

Use physics package

Besides amsmath, you can also use the physics package which provides the \mqty command.

\mqty{... & ... \\ ... & ...}

\mqty

This command creates a matrix quickly inside brackets. Rows and columns are separated in the same way using & and \\.

\mqty*

The starred version gives flexibility for adding brackets or bars depending on your notation style.

\documentclass{article}
\usepackage{physics}
\begin{document}
 \[ \mqty{a & b \\ c & d} \]
\end{document}

Output :

\documentclass{article}
\usepackage{physics}
\begin{document}
 \[\mqty{a & b \\ c & d}
   \quad
   \mqty(a & b \\ c & d)
   \quad
   \mqty*(a & b \\ c & d)
   \quad
   \mqty[a & b \\ c & d]
   \quad
   \mqty|a & b \\ c & d| \]
\end{document}

Output :

Best Practice

Use amsmath for standard matrices as it provides clear control over bracket types.

If you need shorthand commands or quick notations, physics with \mqty is very convenient.