> For the complete documentation index, see [llms.txt](https://overleaf-pro.ayaka.space/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://overleaf-pro.ayaka.space/latex/mathematics/04-matrices.md).

# Matrices

## amsmath matrix environments

The `amsmath` package provides commands to typeset matrices with different delimiters. Once you have loaded `\usepackage{amsmath}` in your preamble, you can use the following environments in your math environments:

| Type                                  | LaTeX markup                                          | Renders as                                          |
| ------------------------------------- | ----------------------------------------------------- | --------------------------------------------------- |
| Plain                                 | `\begin{matrix} 1 & 2 & 3\\ a & b & c \end{matrix}`   | $$\begin{matrix}1 & 2 & 3\a & b & c\end{matrix}$$   |
| <p>Parentheses;<br>round brackets</p> | `\begin{pmatrix} 1 & 2 & 3\\ a & b & c \end{pmatrix}` | $$\begin{pmatrix}1 & 2 & 3\a & b & c\end{pmatrix}$$ |
| <p>Brackets;<br>square brackets</p>   | `\begin{bmatrix} 1 & 2 & 3\\ a & b & c \end{bmatrix}` | $$\begin{bmatrix}1 & 2 & 3\a & b & c\end{bmatrix}$$ |
| <p>Braces;<br>curly brackets</p>      | `\begin{Bmatrix} 1 & 2 & 3\\ a & b & c \end{Bmatrix}` | $$\begin{Bmatrix}1 & 2 & 3\a & b & c\end{Bmatrix}$$ |
| Pipes                                 | `\begin{vmatrix} 1 & 2 & 3\\ a & b & c \end{vmatrix}` | $$\begin{vmatrix}1 & 2 & 3\a & b & c\end{vmatrix}$$ |
| Double pipes                          | `\begin{Vmatrix} 1 & 2 & 3\\ a & b & c \end{Vmatrix}` | $$\begin{Vmatrix}1 & 2 & 3\a & b & c\end{Vmatrix}$$ |

If you need to create matrices with different [delimiters](/latex/mathematics/03-brackets-and-parentheses.md), you can add them manually to a plain `matrix`. For example:

| LaTeX markup                                                                   | Renders as                                                                 |
| ------------------------------------------------------------------------------ | -------------------------------------------------------------------------- |
| `\left\lceil \begin{matrix} 1 & 2 & 3\\ a & b & c \end{matrix} \right\rceil`   | $$\left\lceil\begin{matrix}1 & 2 & 3\a & b & c\end{matrix}\right\rceil$$   |
| `\left\langle \begin{matrix} 1 & 2 & 3\\ a & b & c \end{matrix} \right\rvert`  | $$\left\langle\begin{matrix}1 & 2 & 3\a & b & c\end{matrix}\right\rvert$$  |
| `\left\langle \begin{matrix} 1 & 2 & 3\\ a & b & c \end{matrix} \right\rangle` | $$\left\langle\begin{matrix}1 & 2 & 3\a & b & c\end{matrix}\right\rangle$$ |

## Inline matrices

When typesetting inline math, the usual `matrix` environments above may look too big. It may be better to use `smallmatrix` in such situations, although you will need to provide your own [delimiters](/latex/mathematics/03-brackets-and-parentheses.md).

```latex
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\noindent Trying to typeset an inline matrix here:
 $\begin{pmatrix}
  a & b\\
  c & d
\end{pmatrix}$,
but it looks too big, so let's try
$\big(\begin{smallmatrix}
  a & b\\
  c & d
\end{smallmatrix}\big)$
instead.
\end{document}
```

[Open this `smallmatrix` example in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=amsmath+matrix+example\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cnoindent+Trying+to+typeset+an+inline+matrix+here%3A%0A+%24%5Cbegin%7Bpmatrix%7D%0A++a+%26+b%5C%5C+%0A++c+%26+d%0A%5Cend%7Bpmatrix%7D%24%2C++%0Abut+it+looks+too+big%2C+so+let%27s+try+%0A%24%5Cbig%28%5Cbegin%7Bsmallmatrix%7D%0A++a+%26+b%5C%5C%0A++c+%26+d%0A%5Cend%7Bsmallmatrix%7D%5Cbig%29%24+%0Ainstead.%0A%5Cend%7Bdocument%7D)

The following image shows the output produced by the example above:

![Amsmatrix.png](/files/wFyZsI0lpT0hk01zerT7)

The `mathtools` package provides `psmallmatrix`, `bsmallmatrix` etc environments for convenience.

## Further reading

* [Mathematical expressions](/latex/mathematics/01-mathematical-expressions.md)
* [Brackets and Parentheses](/latex/mathematics/03-brackets-and-parentheses.md)
* [Aligning equations with amsmath](/latex/mathematics/06-aligning-equations-with-amsmath.md)
* [Display style in math mode](/latex/mathematics/10-display-style-in-math-mode.md)
* [The not so short introduction to LaTeX2ε](http://www.ctan.org/tex-archive/info/lshort/)
* [amsmath package documentation](http://texdoc.net/pkg/amsmath)
* [mathtools package documentation](http://texdoc.net/pkg/mathtools)


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