Definition:Matrix/Order

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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.

Others use the term type, but this word can have different connotations.

Some sources do not bother to give the order an actual name, merely referring to, say, an $n \times m$ matrix.


Also see

  • Results about orders of matrices can be found here.


Sources

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