Wolfram Language & System 10.0 (2014)|Legacy Documentation

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gives the generalized outer product of the , forming all possible combinations of the lowestlevel elements in each of them, and feeding them as arguments to f.

treats as separate elements only sublists at level n in the .

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 lowestlevel elements in the remaining will be used.
  • Outer can be used on SparseArray objects, returning a SparseArray object when possible. »
Introduced in 1988
| Updated in 2003