Array
Elementary
An array is an arrangement of objects in rows and columns.
High school
An array is a set of items arranged in rows and columns (or in a list, or in a block with more directions).
Undergraduate (programming)
An array is a collection of elements indexed by tuples of integers $(i_1, \dots, i_k)$ in a rectangular index range. The number $k$ of indices is the number of axes (or dimensions) of the array.
Examples
Examples
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The matrix \(\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}\)
High school
The matrix represents rotation by $90°$ in the standard basis, but it is a grid of numbers, not a function.
Non-examples
Things that may be mistaken for examples.
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Rotation of the plane by $90°$
High school
Rotation of the plane by $90°$ is a function, and different bases give different matrices for it.
Notes
An array is a data structure. Its entries can be any type, and no arithmetic is implied.
Distinctions involving this term
- Array vs. matrix vs. linear map: Grids of numbers appear throughout linear algebra and computing, but a grid can be just data, a matrix with its own arithmetic, or a way of writing a linear map. An array is a grid of data. A matrix is a grid of numbers with matrix arithmetic. A linear map is a function between vector spaces. A matrix represents a linear map as an array of scalars with respect to a given vector basis.