Rank

This page is about array rank, a number associated with every array. For numbers associated with a function specifying its argument rank, see function rank. For the operator that applies a function at a given rank, see Rank operator.

The rank of an array is the number of dimensions in its structure, or, in APL terms, the length of its shape. The traditional expression for the rank of an array A is ⍴⍴A. Because this expression results in a one-element vector rather than a scalar, it is idiomatic in languages with a Tally function to write ≢⍴A instead.

Arrays are given names based on their rank:

Rank	Name
0	scalar
1	vector
2	matrix

Many APLs have a maximum rank. A function that would produce an array with rank greater than this maximum typically gives a LIMIT ERROR.

External Links

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