Definition:Matrix/Also known as
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
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices
- 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation
- 1980: A.J.M. Spencer: Continuum Mechanics ... (previous) ... (next): $2.1$: Matrices: $(2.1)$
- 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 $1.1$
- 1983: K.G. Binmore: Calculus ... (previous) ... (next): $1$ Vectors and matrices: $1.1$ Matrices
- 1998: Richard Kaye and Robert Wilson: Linear Algebra ... (previous) ... (next): Part $\text I$: Matrices and vector spaces: $1$ Matrices: $1.1$ Matrices
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): array: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): matrix (plural matrices)
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.2$: Functions on vectors: $\S 2.2.3$: $m \times n$ matrices
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): array: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): matrix (plural matrices)