This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

Outer

 Outergives the generalized outer product of the , forming all possible combinations of the lowest-level elements in each of them, and feeding them as arguments to f. Outer treats as separate elements only sublists at level n in the . Outer treats as separate elements only sublists at level in the corresponding .
• Outer[Times, list1, list2] gives an outer product.
• The result of applying Outer to the tensors and is the tensor with elements . Applying Outer to two tensors of ranks r and s gives a tensor of rank .
• The heads of all must be the same, but need not necessarily be List. »
• The need not necessarily be cuboidal arrays.
• The specifications of levels must be positive integers, or Infinity.
• If only a single level specification is given, it is assumed to apply to all the . If there are several , but fewer than the number of , the lowest-level elements in the remaining will be used.
Outer product of vectors:
Outer product of matrices:
 Out[1]=

Outer product of vectors:
 Out[1]=
Outer product of matrices:
 Out[2]=
 Scope   (4)
Treat nested lists as rank-1 vectors of sublists:
Arrays can be ragged:
Outer product of SparseArray objects:
The head need not be List:
 Applications   (6)
Word combinations:
Function combinations:
Complete bipartite graph:
Lower-triangular matrix:
Generate all possible binary trees with nodes from and leaves from to depth :
Apply a function on a tensor product grid:
Show a contour plot of the values and the grid:
Include coordinates:
Make a piecewise polynomial that interpolates the data:
The dimensions of the result are a concatenation of the dimensions of the inputs:
Distribute forms the same combinations of all elements, but in a flat structure:
KroneckerProduct is a flattened outer product of matrices:
Part effectively uses an outer product when given lists of parts at multiple levels:
Table can also make a generalized outer product from lists:
If backgrounds are inconsistent, a generalized outer product may not be sparse:
You can convert it into a SparseArray by choosing a background: