请输入您要查询的字词:

 

单词 DotProduct
释义

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:

uv=u1v1+u2v2++unvn.

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

uv=uvcosϑ.

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:

uu=u2
Titledot product
Canonical nameDotProduct
Date of creation2013-03-22 11:46:33
Last modified on2013-03-22 11:46:33
Ownerdrini (3)
Last modified bydrini (3)
Numerical id13
Authordrini (3)
Entry typeDefinition
Classificationmsc 83C05
Classificationmsc 15A63
Classificationmsc 14-02
Classificationmsc 14-01
Synonymscalar product
Related topicCauchySchwarzInequality
Related topicCrossProduct
Related topicVector
Related topicDyadProduct
Related topicInvariantScalarProduct
Related topicAngleBetweenLineAndPlane
Related topicTripleScalarProduct
Related topicProvingThalesTheoremWithVectors
Definesscalar square
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 20:06:43