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

FilledSmallSquarea.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.

FilledSmallSquare Various applications of Dot:

FilledSmallSquare Examples: a, b . c, d LongRightArrow.

FilledSmallSquarea, b, c, d . x, y LongRightArrow.

FilledSmallSquare 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.

FilledSmallSquare When its arguments are not lists, Dot remains unevaluated. It has the attribute Flat.

FilledSmallSquare See The Mathematica Book: Section 1.8.3 and Section 3.7.5.

FilledSmallSquare See also: Inner, Cross, Outer, NonCommutativeMultiply.

FilledSmallSquare Related package: Calculus`VectorAnalysis`.

Further Examples