Matrices and arrays

A matrix in LaTeX is a grid of cells: & separates the columns, \\ separates the rows, and an environment wraps the grid in the right pair of delimiters. The matrix environments come from amsmath, so that package needs to be in your preamble before any of this compiles.

\begin{pmatrix} a & b \\ c & d \end{pmatrix} % ( )
\begin{bmatrix} a & b \\ c & d \end{bmatrix} % [ ]
\begin{vmatrix} a & b \\ c & d \end{vmatrix} % | |

The matrix environments

All three share the same body; only the surrounding delimiters change. pmatrix wraps the grid in parentheses, the most common style for matrices and vectors. bmatrix uses square brackets, and vmatrix uses single vertical bars, the standard notation for a determinant. There is also plain matrix with no delimiters, Bmatrix with braces, and Vmatrix with double bars for norms. Inside, a & b fills the two columns of a row, \\ starts the next row, and every row should carry the same number of & separators.

These environments must appear inside math mode; wrap them in \[ ... \] or use them within an equation. For a small matrix in the middle of a sentence, smallmatrix, also from amsmath, sets a compact version that does not stretch the line: $\bigl(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\bigr)$.

Custom array

\begin{array}{r|cc}
 1 & 2 & 3 \\
 \hline
 4 & 5 & 6
\end{array}

When you need per-column control, array is the general tool. Its mandatory argument is a column specification: here r|cc declares a right-aligned column, a vertical rule, then two centered columns. The alignment letters are l, c, and r, and | draws a rule between columns. \hline between rows draws a horizontal rule across the full width. array draws no outer delimiters of its own; pair it with \left( and \right) if you want them. It is the math-mode sibling of the tabular environment used for tables in text.

Common mistakes

The error “Extra alignment tab has been changed to \cr” means a row has more & separators than the column count allows, which usually traces back to a missing \\ at the end of the previous row. “Environment pmatrix undefined” means \usepackage{amsmath} is missing. A matrix pasted outside math mode fails with “Missing $ inserted”; see math mode basics if the delimiters are new. Comparing a two-by-two in each delimiter style takes seconds in the live playground.