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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]= 
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | | | |
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