# Array

Array[f,n]

generates a list of length n, with elements f[i].

Array[f,n,r]

generates a list using the index origin r.

Array[f,n,{a,b}]

generates a list using n values from a to b.

Array[f,{n1,n2,}]

generates an n1×n2× array of nested lists, with elements f[i1,i2,].

Array[f,{n1,n2,},{r1,r2,}]

generates a list using the index origins ri (default 1).

Array[f,{n1,n2,},{{a1,b1},{a2,b2},}]

generates a list using ni values from ai to bi.

Array[f,dims,origin,h]

uses head h, rather than List, for each level of the array.

# Examples

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## Basic Examples(4)

Generate a 3×2 array:

Generate a 3×4 array:

Use index origin 0 instead of 1:

Sample between 0 and 1:

Use ranges {-1/2,1/2} and {0,1}:

## Generalizations & Extensions(2)

Use ## to pick up a sequence of indices:

Use Plus instead of List to combine elements:

## Applications(5)

3×3 matrix of 0s:

Totally antisymmetric tensor:

Lower-triangular matrix:

Matrix with generic symbolic entries:

Use it to see the effects of some linear algebra functions:

Sample a function uniformly on an interval:

## Properties & Relations(3)

ConstantArray[c,dims] and Array[c&,dims] are equivalent:

When c is a machine number, ConstantArray is much faster for large arrays:

Array[f,dims] can be generated using Table:

Set up the Table limit specifications:

Use Apply to splice them into a Table command:

The result is identical to the array generated using Array:

SparseArray[{i_,j_}->f[i,j],dims] gives a sparse representation of Array[f,dims]:

The results are Equal:

The objects are not identical, but the represented arrays are:

## Neat Examples(3)

Array of powers:

Array of GCDs:

Array of arrays:

Wolfram Research (1988), Array, Wolfram Language function, https://reference.wolfram.com/language/ref/Array.html (updated 2012).

#### Text

Wolfram Research (1988), Array, Wolfram Language function, https://reference.wolfram.com/language/ref/Array.html (updated 2012).

#### BibTeX

@misc{reference.wolfram_2021_array, author="Wolfram Research", title="{Array}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Array.html}", note=[Accessed: 27-September-2021 ]}

#### BibLaTeX

@online{reference.wolfram_2021_array, organization={Wolfram Research}, title={Array}, year={2012}, url={https://reference.wolfram.com/language/ref/Array.html}, note=[Accessed: 27-September-2021 ]}

#### CMS

Wolfram Language. 1988. "Array." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/Array.html.

#### APA

Wolfram Language. (1988). Array. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Array.html