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Dot
a
.
b
.
c or Dot[
a
,
b
,
c
] gives products of vectors, matrices and tensors.
a
.
b gives an explicit result when a and b are lists with appropriate dimensions. It contracts the last index in a with the first index in b.
Various applications of Dot:
Examples: 
a, b
.
c, d
  .
a, b
,
c, d
.
x, y
 .
The result of applying Dot to two tensors  and  is the tensor  . Applying Dot to a rank  tensor and a rank  tensor gives a rank  tensor.
When its arguments are not lists, Dot remains unevaluated. It has the attribute Flat.
See the Mathematica book: Section 1.8.3, Section 3.7.5.
See also: Inner, Cross, Outer, NonCommutativeMultiply.
Related package: Calculus`VectorAnalysis`.
Further Examples
This is the dot product of two vectors.
In[1]:= 
Out[1]= 
This is the dot product of a  x  matrix and a vector.
In[2]:= 
Out[2]= 
The dot product of a  x  matrix and a  x  matrix is a  x  matrix.
In[3]:= 
Out[3]//MatrixForm= 
This is the dot product of two tensors.
In[4]:= 
In[5]:= 
In[6]:= 
Out[6]= 
Here are their dimensions.
In[7]:= 
Out[7]= 
In[8]:= 
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