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Documentation / Mathematica / Built-in Functions / Lists and Matrices / Vector Operations /

Dot

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

FilledSmallSquare 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.

FilledSmallSquare Various applications of Dot:

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

FilledSmallSquare a, 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 Dot can be used on SparseArray objects, returning a SparseArray object when possible.

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

FilledSmallSquare See Section 1.8.3 and Section 3.7.5.

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

FilledSmallSquare Related package: Calculus`VectorAnalysis`.

FilledSmallSquare New in Version 1.

Further Examples