Basic Matrix Types

LaTeX offers various matrix environments, each with different delimiters:

1. matrix Environment (no delimiters)

2. pmatrix Environment (parentheses)

3. bmatrix Environment (square brackets)

4. vmatrix Environment (vertical bars — determinants)

5. Bmatrix Environment (curly braces)

6. Vmatrix Environment (double bars — norms)

The naming is consistent: the letter before matrix tells you the delimiter. Lowercase gives you the ordinary bracket (pmatrix → parentheses, vmatrix → single bars) and uppercase gives you the “bigger” variant (Bmatrix → braces, Vmatrix → double bars).

Inside all of them, & separates columns and \\ ends a row. There is no \\ after the final row — adding one creates an empty trailing row, which shows up as unexpected vertical space inside the brackets.

Matrix with Alignment

You can control column alignment using the array environment:

The {lcr} specifies left, center, and right alignment for each column.

Augmented Matrices

For systems of equations, you can create augmented matrices using the array environment:

The vertical line in {cc|c} creates the augmentation line.

Inline Matrices with smallmatrix

A full matrix environment inside a sentence pushes the surrounding lines apart. Use smallmatrix instead — it typesets at script size and leaves line spacing intact, so it sits inline in a sentence like $\left(\begin{smallmatrix} 0 & -1 \\ 1 & 0 \end{smallmatrix}\right)$:

smallmatrix draws no delimiters of its own, so wrap it in \left( and \right) yourself.

Multiplying Matrices

The product of an m × n matrix and an n × r matrix is defined entry by entry as a sum over the shared dimension:

Written out, the intermediate sums are worth keeping visible while you check the arithmetic:

Three Errors That Break Most Matrices

Missing $ inserted

Matrix environments only work in math mode. Writing \begin{bmatrix} in ordinary text produces this error. Wrap it in \[ ... \] for a displayed matrix or $ ... $ for an inline one.

Extra alignment tab has been changed to \cr

A row has more & separators than the matrix has columns — usually one stray & at the end of a row. A three-column matrix needs exactly two separators per row.

Brackets that do not stretch

If your delimiters are the wrong height you have probably typed literal [ and ] characters. Either use the matching environment (bmatrix) or pair \left[ with \right] so LaTeX sizes them to the content.

Advanced Matrix Features

• Dots in Matrices

• Nested Matrices

• Matrix with Text

Best Practices

• Use \begin{array} when you need precise control over column alignment
• Use \begin{pmatrix} or \begin{bmatrix} for standard matrices
• Use \begin{smallmatrix} for inline matrices to maintain proper line spacing
• Use \vdots, \ddots, and \cdots for professional-looking ellipses