Column — Definition, Formula & Examples

A column is a vertical line of numbers running from top to bottom in a matrix or table. Each column holds one value from every row.

In an $m \times n$ matrix $A$ , a column is the ordered list of $m$ entries sharing the same position index $j$ , written as $a_{1j}, a_{2j}, \ldots, a_{mj}$ for a fixed $j$ between $1$ and $n$ .

How It Works

To find a column, look at the entries that line up vertically. The first column contains every entry in position 1 of each row, the second column contains every entry in position 2, and so on. An

m \times n

matrix has exactly

n

columns, each containing

m

entries.

Worked Example

Problem: Identify the columns of the matrix below.

The matrix: Consider this 2 × 3 matrix:

A = \begin{bmatrix} 4 & 7 & 1 \\ 3 & 5 & 8 \end{bmatrix}

Column 1: Read the first entry from each row going top to bottom.

\begin{bmatrix} 4 \\ 3 \end{bmatrix}

Column 2: Read the second entry from each row.

\begin{bmatrix} 7 \\ 5 \end{bmatrix}

Column 3: Read the third entry from each row.

\begin{bmatrix} 1 \\ 8 \end{bmatrix}

Answer: Matrix A has 3 columns: [4, 3], [7, 5], and [1, 8].

Why It Matters

Knowing which entries form a column is essential when you multiply matrices, since each result comes from pairing a row of one matrix with a column of another. Columns also appear in data tables and spreadsheets, where each column represents a different category or variable.

Common Mistakes

Mistake: Confusing columns with rows.

Correction: Columns go top to bottom (vertical), while rows go left to right (horizontal). Think of the columns that hold up a building — they stand upright.