# Definition:Matrix/Order

## Definition

Let $\sqbrk a_{m n}$ be an $m \times n$ matrix.

Then the parameters $m$ and $n$ are known as the **order** of the matrix.

### Square Matrix

Let $\mathbf A$ be an $n \times n$ square matrix.

That is, let $\mathbf A$ have $n$ rows (and by definition $n$ columns).

Then the **order** of $\mathbf A$ is defined as being $n$.

### Column Matrix

Let $\mathbf A$ be an $n \times 1$ column matrix.

Then the **order** of $\mathbf A$ is defined as being $n$.

### Row Matrix

Let $\mathbf A$ be a $1 \times n$ row matrix.

Then the **order** of $\mathbf A$ is defined as being $n$.

## Also known as

The **order** of a matrix can also be referred to as its **dimensions**, but the term **dimension** has a different, deeper meaning in linear algebra and this may be a source of confusion.

Some sources refer to the **size** rather than **order**, which is acceptable enough.

## Sources

- 1954: A.C. Aitken:
*Determinants and Matrices*(8th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions and Fundamental Operations of Matrices: $3$. The Notation of Matrices - 1982: A.O. Morris:
*Linear Algebra: An Introduction*(2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.2$ Elementary Row Operations on Matrices: Definition $1.1$ - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**order**:**8.**(of a matrix) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**order**(of a matrix)