# Dot a.b.c or Dot[a,b,c]

gives products of vectors, matrices, and tensors.

# Details • 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 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.

# Examples

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## Basic Examples(3)

Scalar product of vectors:

 In:= Out= Products of matrices and vectors:

 In:= Out= In:= Out= In:= Out= Matrix product:

 In:= Out= ## Possible Issues(3)

Introduced in 1988
(1.0)
|
Updated in 2003
(5.0)