Dot

or Dot[a, b, c]
gives products of vectors, matrices, and tensors.

DetailsDetails

  • 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:
  • {a1,a2}.{b1,b2}scalar product of vectors
    {a1,a2}.{{m11,m12},{m21,m22}}
    product of a vector and a matrix
    {{m11,m12},{m21,m22}}.{a1,a2}
    product of a matrix and a vector
    {{m11,m12},{m21,m22}}.{{n11,n12},{n21,n22}}
    product of two matrices
  • 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. »
  • Dot can be used on SparseArray objects, returning a SparseArray object when possible. »
  • When its arguments are not lists or sparse arrays, Dot remains unevaluated. It has the attribute Flat.
New in 1 | Last modified in 5
New to Mathematica? Find your learning path »
Have a question? Ask support »