Definition:Matrix/Also known as

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Matrix: Also known as

A matrix is often considered as an array of two dimensions.

However, the usual convention nowadays is to reserve the term array for the written-down denotation of a matrix.


The notation $\mathbf A = \sqbrk a_{m n}$ is a notation which is not yet seen frequently.

$\mathbf A = \paren {a_{i j} }_{m \times n}$ or $\mathbf A = \paren {a_{i j} }$ are more common.

However, the notation $\sqbrk a_{m n}$ is gaining in popularity because it better encapsulates the actual order of the matrix itself in the notational form.


Some use the similar notation $\sqbrk {a_{m n} }$, moving the subscripts into the brackets.


Some sources use round brackets to encompass the array, thus:

$\quad \mathbf A = \begin{pmatrix} a_{1 1} & a_{1 2} & \cdots & a_{1 n} \\ a_{2 1} & a_{2 2} & \cdots & a_{2 n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m 1} & a_{m 2} & \cdots & a_{m n} \\ \end{pmatrix}$

Which is used is ultimately no more than a matter of taste.


When writing a row matrix or column matrix as an array, the index of the row (for the row matrix) or column (for the column matrix) are usually left out, as the implicit $1$ is taken as understood.


Sources

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