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): order: 8. (of a matrix)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): order (of a matrix)