dot product

Let u=(u1,u2,,un) and v=(v1,v2,,vn) two vectors on kn where k is a field (like or ). Then we define the dot productMathworldPlanetmath of the two vectors as:


Notice that uv is NOT a vector but a scalar (an element from the field k).

If u,v are vectors in n and ϑ is the angle between them, then we also have


Thus, in this case, uv if and only if uv=0.

The special case  uu  of scalar product is the scalar square of the vector u.  In n it equals to the square of the length of u:

Title dot product
Canonical name DotProduct
Date of creation 2013-03-22 11:46:33
Last modified on 2013-03-22 11:46:33
Owner drini (3)
Last modified by drini (3)
Numerical id 13
Author drini (3)
Entry type Definition
Classification msc 83C05
Classification msc 15A63
Classification msc 14-02
Classification msc 14-01
Synonym scalar product
Related topic CauchySchwarzInequality
Related topic CrossProduct
Related topic Vector
Related topic DyadProduct
Related topic InvariantScalarProduct
Related topic AngleBetweenLineAndPlane
Related topic TripleScalarProduct
Related topic ProvingThalesTheoremWithVectors
Defines scalar square