Matrices in LaTeX: pmatrix, bmatrix, vmatrix

Inside math, use \begin{pmatrix} ... \end{pmatrix} for a matrix in parentheses, with & between the entries of a row and \\ between rows. bmatrix gives square brackets and vmatrix vertical bars for a determinant.

A first matrix

Matrix environments come from the amsmath package and are used inside math. Entries in a row are separated by &, rows end with \\. Each column is centred.

A = \begin{pmatrix}
  1 & 2 \\
  3 & 4
\end{pmatrix}

Brackets

The environment name sets the brackets around the matrix:

\begin{matrix} a & b \\ c & d \end{matrix} \quad
\begin{pmatrix} a & b \\ c & d \end{pmatrix} \quad
\begin{bmatrix} a & b \\ c & d \end{bmatrix} \quad
\begin{Bmatrix} a & b \\ c & d \end{Bmatrix} \quad
\begin{vmatrix} a & b \\ c & d \end{vmatrix} \quad
\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}

A norm can also be written with the double bars around a plain matrix, which gives the same result:

\begin{Vmatrix} 3 \\ 4 \end{Vmatrix} = \left\| \begin{matrix} 3 \\ 4 \end{matrix} \right\| = 5

Determinants

A determinant is a vmatrix. Write \det for the upright function name.

\det \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

Large matrices with dots

\cdots (horizontal), \vdots (vertical) and \ddots (diagonal) stand for the entries you leave out.

A = \begin{pmatrix}
  a_{11} & a_{12} & \cdots & a_{1n} \\
  a_{21} & a_{22} & \cdots & a_{2n} \\
  \vdots & \vdots & \ddots & \vdots \\
  a_{m1} & a_{m2} & \cdots & a_{mn}
\end{pmatrix}

Vectors

A column vector is a matrix with one column. For a row vector, write one row.

\mathbf{v} = \begin{pmatrix} 4 \\ 4 \\ 2 \end{pmatrix}, \qquad
\mathbf{w}^\top = \begin{pmatrix} 1 & 0 & -1 \end{pmatrix}, \qquad
\mathbf{w}^\top \mathbf{v} = 2

Small matrices in the text

smallmatrix sets a matrix small enough for a line of text. It has no brackets of its own, so add them with \left( and \right).

The rotation by 90 degrees is
$R = \left(\begin{smallmatrix} 0 & -1 \\ 1 & 0 \end{smallmatrix}\right)$,
and $R^2 = -I$.

array: your own column alignment

The array environment works like tabular, but in math: the argument gives the alignment of each column (l, c, r).

\left( \begin{array}{rl}
  -44 & x \\
    2 & xyz
\end{array} \right)

\left[ \begin{array}{cccc}
  1 & 2 & | & 4 \\
  0 & 1 & | & 4
\end{array} \right]

What differs from a TeX installation

More on the amsmath page and the mathtools page. The full manuals are at ctan.org/pkg/amsmath and ctan.org/pkg/mathtools.

To build a matrix by clicking instead of typing, use the LaTeX matrix generator; it writes the pmatrix or bmatrix source for you.

Every example on this page is typeset by Scissor LaTeX when the site is built. Last updated 2026-11-06.