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
SearchNetworking
  • network packet

    A network packet is a basic unit of data that's grouped together and transferred over a computer network, typically a ...

  • virtual network functions (VNFs)

    Virtual network functions (VNFs) are virtualized tasks formerly carried out by proprietary, dedicated hardware.

  • network functions virtualization (NFV)

    Network functions virtualization (NFV) is a network architecture model designed to virtualize network services that have ...

SearchSecurity
  • What is cybersecurity?

    Cybersecurity is the protection of internet-connected systems such as hardware, software and data from cyberthreats.

  • Android System WebView

    Android System WebView is a system component for the Android operating system (OS) that allows Android apps to display web ...

  • data masking

    Data masking is a method of creating a structurally similar but inauthentic version of an organization's data that can be used ...

SearchCIO
  • privacy compliance

    Privacy compliance is a company's accordance with established personal information protection guidelines, specifications or ...

  • contingent workforce

    A contingent workforce is a labor pool whose members are hired by an organization on an on-demand basis.

  • product development (new product development -- NPD)

    Product development, also called new product management, is a series of steps that includes the conceptualization, design, ...

SearchHRSoftware
  • talent acquisition

    Talent acquisition is the strategic process employers use to analyze their long-term talent needs in the context of business ...

  • employee retention

    Employee retention is the organizational goal of keeping productive and talented workers and reducing turnover by fostering a ...

  • hybrid work model

    A hybrid work model is a workforce structure that includes employees who work remotely and those who work on site, in a company's...

SearchCustomerExperience
  • Salesforce Trailhead

    Salesforce Trailhead is a series of online tutorials that coach beginner and intermediate developers who need to learn how to ...

  • Salesforce

    Salesforce, Inc. is a cloud computing and social enterprise software-as-a-service (SaaS) provider based in San Francisco.

  • data clean room

    A data clean room is a technology service that helps content platforms keep first person user data private when interacting with ...

Close