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
open all close allIntroduced in 1988
Updated in 2003
(1.0)
|
(5.0)