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 Documentation / Mathematica / Built-in Functions / Lists and Matrices / Matrix Operations  /
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 1.8.3Section 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]:=