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Outer

Outer[f, list1, list2, ...]
gives the generalized outer product of the listi, forming all possible combinations of the lowest-level elements in each of them, and feeding them as arguments to f.
Outer[f, list1, list2, ..., n]
treats as separate elements only sublists at level n in the listi.
Outer[f, list1, list2, ..., n1, n2, ...]
treats as separate elements only sublists at level ni in the corresponding listi.
  • Outer[Times, list1, list2] gives an outer product.
  • The result of applying Outer to the tensors Ti1i2...ir and Uj1j2...js is the tensor Vi1i2...irj1j2...js with elements f[Ti1i2...ir, Uj1j2...js]. Applying Outer to two tensors of ranks r and s gives a tensor of rank r+s.
  • The heads of all listi must be the same, but need not necessarily be List.  »
  • The listi need not necessarily be cuboidal arrays.
  • The specifications ni of levels must be positive integers, or Infinity.
  • If only a single level specification is given, it is assumed to apply to all the listi. If there are several ni, but fewer than the number of listi, the lowest-level elements in the remaining listi will be used.
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