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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.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Array Element Specification  
Index Specification  
Head Specification  
Applications  
Properties & Relations  
Neat Examples  
See Also
Tech Notes
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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.

Details

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:

Start with indices 0 and 4 instead of 1:

Sample between 0 and 1:

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

Scope  (11)

Array Element Specification  (5)

Create a 3×2 array using an indexed symbol:

Create a 4×4 array using a subscript:

Create a Hilbert matrix:

Use named function slots:

Compare with the built-in function:

Create a constant array:

Use ## to pick up a sequence of indices:

Index Specification  (4)

Create a 1D array:

Create a 1D array, starting the indices at 0:

Create a 3×2 array:

Create a 4×3×2 array with index-dependent origins:

Head Specification  (2)

Use a non-default head for each level of the array:

Use Plus instead of List to combine elements:

Any symbol with attribute Flat would produce the same shape:

Applications  (4)

Totally antisymmetric tensor:

Compare with the built-in LeviCivitaTensor:

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  (4)

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:

Compute Array in parallel:

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).

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

BibTeX

@misc{reference.wolfram_2025_array, author="Wolfram Research", title="{Array}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Array.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_array, organization={Wolfram Research}, title={Array}, year={2012}, url={https://reference.wolfram.com/language/ref/Array.html}, note=[Accessed: 01-December-2025]}