This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 Inner Inner[ f , , , g ] is a generalization of Dot in which f plays the role of multiplication and g of addition. Example: Inner[f, a,b , x,y ,g]. Inner[f, a,b , c,d , x,y ,g]. Like Dot, Inner effectively contracts the last index of the first tensor with the first index of the second tensor. Applying Inner to a rank tensor and a rank tensor gives a rank tensor. Inner[ f , , ] uses Plus for g. Inner[ f , , , g , n ] contracts index n of the first tensor with the first index of the second tensor. The heads of and must be the same, but need not necessarily be List. See the Mathematica book: Section 2.2.10, Section 3.7.11. See also: Outer, Thread, MapThread. Further Examples Here is another way (beside Dot) to get the dot product of two vectors. In[1]:= Out[1]= This is a generalized inner product. In[2]:= Out[2]= This gives the inner product of two tensors and shows their ranks. In[3]:= In[4]:= In[5]:= Out[5]= In[6]:= Out[6]=