Browse Definitions :

absolute value

Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system. This can apply to scalar or vector quantities. The symbol for absolute value is a pair of vertical lines, one on either side of the quantity whose absolute value is to be determined.

Suppose x is a real number. Then the absolute value of x is defined as follows:

For x = 0 or x > 0, | x | = x
For x < 0, | x | = - x

Alternatively, the absolute value of a real number x is equal to the positive square root of x 2 :

| x | = ( x 2 ) 1/2

Let a + jb be a complex number, where a and b are real numbers and j is the positive square root of -1. (The symbol j is standard in engineering practice; mathematicians symbolize the positive square root of -1 as i .) Then the absolute value of a + jb , also called the modulus, is defined as follows:

| a + jb | = ( a 2 + b 2 ) 1/2

The absolute value of a vector in n dimensions is defined in terms of the coordinates of its termination point, in Cartesian n -space, assuming its origin coincides with the point where all coordinate values are zero. Suppose v is a vector in n dimensions, represented by the following coordinates:

v = ( v 1 , v 2 , v 3 , ..., v n )

Then the absolute value of v is given by:

| v | = ( v 1 2 + v 2 2 + v 3 2 + ... + v n 2 ) 1/2

Also see Mathematical Symbols .

This was last updated in November 2010

Join the conversation

1 comment

Send me notifications when other members comment.

Please create a username to comment.

Who were the scientists that first developed this?


File Extensions and File Formats

Powered by:


  • risk assessment

    Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business.

  • PCI DSS (Payment Card Industry Data Security Standard)

    The Payment Card Industry Data Security Standard (PCI DSS) is a widely accepted set of policies and procedures intended to ...

  • risk management

    Risk management is the process of identifying, assessing and controlling threats to an organization's capital and earnings.



  • telemedicine (telehealth)

    Telemedicine is the remote delivery of healthcare services, such as health assessments or consultations, over the ...

  • Project Nightingale

    Project Nightingale is a controversial partnership between Google and Ascension, the second largest health system in the United ...

  • medical practice management (MPM) software

    Medical practice management (MPM) software is a collection of computerized services used by healthcare professionals and ...



  • hot plugging

    Hot plugging is the addition of a component to a running computer system without significant interruption to the operation of the...

  • M.2 SSD

    An M.2 SSD is a solid-state drive (SSD) that conforms to a computer industry specification and is used in internally mounted ...

  • kilobyte (KB or Kbyte)

    A kilobyte (KB or Kbyte) is a unit of measurement for computer memory or data storage used by mathematics and computer science ...