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:

Examples: a, b . c, d .

a, b, c, d . x, y .

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.

See Section 1.8.3 and Section 3.7.5.

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

Related package: Calculus`VectorAnalysis`.

New in Version 1.

Further Examples