This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 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]:=