Editing Outer product (section)

==In programming languages==
In some programming languages, given a two-argument function <code>f</code> (or a binary operator), the outer product, <code>f</code>, of two one-dimensional arrays, <code>A</code> and <code>B</code>, is a two-dimensional array <code>C</code> such that <code>C[i, j] = f(A[i], B[j])</code>. This is syntactically represented in various ways: in [[APL (programming language)|APL]], as the infix binary operator <syntaxhighlight lang=apl inline>∘.f</syntaxhighlight>; in [[J (programming language)|J]], as the postfix adverb <syntaxhighlight lang=j inline>f/</syntaxhighlight>; in [[R (programming language)|R]], as the function <syntaxhighlight lang=r inline>outer(A, B, f)</syntaxhighlight> or the special <syntaxhighlight lang=r inline>%o%</syntaxhighlight>;<ref>{{cite web |title=outer function {{!}} R Documentation |url=https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/outer|access-date=2020-09-07 |website=rdocumentation.org}}</ref> in [[Wolfram Mathematica|Mathematica]], as <syntaxhighlight lang=mathematica inline>Outer[f, A, B]</syntaxhighlight>. In [[MATLAB]], the function <syntaxhighlight lang=matlab inline>kron(A, B)</syntaxhighlight> is used for this product. These often generalize to multi-dimensional arguments, and more than two arguments.

In the [[Python (programming language)|Python]] library [[NumPy]], the outer product can be computed with function <code>np.outer()</code>.<ref>{{cite web |title=numpy.outer — NumPy v1.19 Manual |url=https://numpy.org/doc/stable/reference/generated/numpy.outer.html |access-date=2020-09-07 |website=numpy.org}}</ref> In contrast, <code>np.kron</code> results in a flat array. The outer product of multidimensional arrays can be computed using <code>np.multiply.outer</code>.