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Dot

Usage

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


Notes

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:
{ ,  } . { ,  } scalar product of vectors
{ ,  } . {{ ,  }, { ,  }} product of a vector and a matrix
{{ ,  }, { ,  }} . { ,  } product of a matrix and a vector
{{ ,  }, { ,  }} . {{ ,  }, { ,  }} product of two matrices
• Examples:  a, b .  c, d LongRightArrow .
  a, b ,  c, d  .  x, y LongRightArrow .
• 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.
• Related package: Calculus`VectorAnalysis`.
• New in Version 1.
• Advanced Documentation.


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