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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:
{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 T_(i_1 i_2... i_n) and U_(j_1 j_2... j_m) is the tensor . Applying Dot to a rank n tensor and a rank m tensor gives a rank m+n-2 tensor.  »
  • When its arguments are not lists or sparse arrays, Dot remains unevaluated. It has the attribute Flat.
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