Browse Definitions :
Definition

dot product (scalar product)

The dot product, also called the scalar product, of two vector s is a number ( scalar quantity) obtained by performing a specific operation on the vector components. The dot product has meaning only for pairs of vectors having the same number of dimensions. The symbol for dot product is a heavy dot ( ).

In the two-dimensional Cartesian plane, vectors are expressed in terms of the x -coordinates and y -coordinates of their end points, assuming they begin at the origin ( x , y ) = (0,0). Some examples are shown in the illustration below.

The dot product of two vectors is determined by multiplying their x -coordinates, then multiplying their y -coordinates, and finally adding the two products. Thus, in the above example:

A B = (2 x -4) + (5 x -3) = -8 - 15 = -23

B C = (-4 x 5) + (-3 x -5) = -20 + 15 = -5

C A = (5 x 2) + (-5 x 5) = 10 - 25 = -15

In polar coordinates, vectors are expressed in terms of length (magnitude) and direction. When expressed in this format, the dot product of two vectors is equal to the product of their lengths, multiplied by the cosine of the angle between them.

For any two vectors A and B , A B = B A . That is, the dot product operation is commutative; it does not matter in which order the operation is performed.

Also see Fast Reference for Math Symbols .

This was last updated in March 2011
SearchCompliance
  • compliance risk

    Compliance risk is an organization's potential exposure to legal penalties, financial forfeiture and material loss, resulting ...

  • information governance

    Information governance is a holistic approach to managing corporate information by implementing processes, roles, controls and ...

  • enterprise document management (EDM)

    Enterprise document management (EDM) is a strategy for overseeing an organization's paper and electronic documents so they can be...

SearchSecurity
  • IPsec (Internet Protocol Security)

    IPsec (Internet Protocol Security) is a suite of protocols and algorithms for securing data transmitted over the internet or any ...

  • principle of least privilege (POLP)

    The principle of least privilege (POLP) is a concept in computer security that limits users' access rights to only what are ...

  • biometric authentication

    Biometric authentication is a security process that relies on the unique biological characteristics of individuals to verify they...

SearchHealthIT
SearchDisasterRecovery
  • risk mitigation

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • call tree

    A call tree is a layered hierarchical communication model that is used to notify specific individuals of an event and coordinate ...

  • Disaster Recovery as a Service (DRaaS)

    Disaster recovery as a service (DRaaS) is the replication and hosting of physical or virtual servers by a third party to provide ...

SearchStorage
  • cloud storage

    Cloud storage is a service model in which data is transmitted and stored on remote storage systems, where it is maintained, ...

  • cloud testing

    Cloud testing is the process of using the cloud computing resources of a third-party service provider to test software ...

  • storage virtualization

    Storage virtualization is the pooling of physical storage from multiple storage devices into what appears to be a single storage ...

Close