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
• ISO 31000 Risk Management

The ISO 31000 Risk Management framework is an international standard that provides businesses with guidelines and principles for ...

• pure risk

Pure risk refers to risks that are beyond human control and result in a loss or no loss with no possibility of financial gain.

• risk reporting

Risk reporting is a method of identifying risks tied to or potentially impacting an organization's business processes.

• walled garden

On the internet, a walled garden is an environment that controls the user's access to network-based content and services.

• potentially unwanted program (PUP)

A potentially unwanted program (PUP) is a program that may be unwanted, despite the possibility that users consented to download ...

• plaintext

In cryptography, plaintext is usually ordinary readable text before it is encrypted into ciphertext or after it is decrypted.

• What is risk mitigation?

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

• fault-tolerant

Fault-tolerant technology is a capability of a computer system, electronic system or network to deliver uninterrupted service, ...

• synchronous replication

Synchronous replication is the process of copying data over a storage area network, local area network or wide area network so ...

• Remote Direct Memory Access (RDMA)

Remote Direct Memory Access (RDMA) is a technology that enables two networked computers to exchange data in main memory without ...

• storage (computer storage)

Data storage is the collective methods and technologies that capture and retain digital information on electromagnetic, optical ...

• storage medium (storage media)

In computers, a storage medium is a physical device that receives and retains electronic data for applications and users and ...

Close