Built-in Mathematica Symbol

Array

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

Array[f, {n₁, n₂, ...}]
generates an

array of nested lists, with elements f[i₁, i₂, ...].

Array[f, {n₁, n₂, ...}, {r₁, r₂, ...}]
generates a list using the index origins r_i (default 1).

Array[f, dims, origin, h]
uses head h, rather than List, for each level of the array.

EXAMPLES

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Basic Examples (3)

Generate a

array:

Generate a

array:

Use index origin 0 instead of 1:

Start with indices 0 and 4 instead of 1:

Generate a

array:

In[1]:=

Out[1]=

Generate a

array:

In[2]:=

Out[2]=

Use index origin 0 instead of 1:

In[1]:=

Out[1]=

Start with indices 0 and 4 instead of 1:

In[2]:=

Out[2]=

Generalizations & Extensions (2)

Use ## to pick up a sequence of indices:

Use Plus instead of List to combine elements:

Applications (4)

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:

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: