Matrix dimensions

The dimensions of a matrix are the number of rows and columns it has.

Dimensions of a matrix

We write the dimensions of a matrix as m \times n, where m is the number of rows and n is the number of columns.

For example, this matrix has 2 rows and 3 columns, so its dimensions are 2 \times 3:

\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}

Dimensions of a row vector

A row vector only has one, well, row. So a row vector with 4 columns has dimensions 1 \times 4.

A row vector might look something like this:

\begin{bmatrix} 1 & 2 & 3 & 4 \end{bmatrix}

Dimensions of a column vector

A column vector only has one column. So that means that a column vector with 3 rows has dimensions 3 \times 1.

Column vectors look like this, for example:

\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}

Dimensions of a square matrix

If we have a square matrix, it has the same number of rows and columns. So a square matrix with 4 rows and 4 columns has dimensions 4 \times 4.

A square matrix might look like this, a 4 \times 4 matrix:

\begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \end{bmatrix}

Or, like this, a 2 \times 2 matrix:

\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

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