Arabic Bulgarian Chinese Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hindi Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Malagasy Norwegian Persian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Thai Turkish Vietnamese
Arabic Bulgarian Chinese Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hindi Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Malagasy Norwegian Persian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Thai Turkish Vietnamese

definition - Magnitude (mathematics)

definition of Wikipedia

   Advertizing ▼


Magnitude (mathematics)


In mathematics, magnitude is the "size" of a mathematical object, a property by which the object can be compared as larger or smaller than other objects of the same kind. More formally, an object's magnitude is an ordering (or ranking) of the class of objects to which it belongs.



The Greeks distinguished between several types of magnitude,[citation needed] including:

They proved that the first two could not be the same, or even isomorphic systems of magnitude.[citation needed] They did not consider negative magnitudes to be meaningful, and magnitude is still chiefly used in contexts in which zero is either the lowest size or less than all possible sizes.


The magnitude of any number x is usually called its "absolute value" or "modulus", denoted by |x|.

  Real numbers

The absolute value of a real number r is defined by:

|r| = r, if r ≥ 0
|r| = -r, if r < 0.

It may be thought of as the number's distance from zero on the real number line. For example, the absolute value of both 7 and −7 is 7.

  Complex numbers

A complex number z may be viewed as the position of a point P in a 2-dimensional space, called the complex plane. The absolute value of z may be thought of as the distance of P from the origin of that space. The formula for the absolute value of z is similar to that for the Euclidean norm of a vector in a 2-dimensional Euclidean space:

 \left| z \right| = \sqrt{\Re(z)^2 + \Im(z)^2 }

where ℜ(z) and ℑ(z) are the respectively real part and imaginary part of z. For instance, the modulus of −3 + 4i is 5.

  Euclidean vectors

A Euclidean vector represents the position of a point P in a Euclidean space. Geometrically, it can be described as an arrow from the origin of the space (vector tail) to that point (vector tip). Mathematically, a vector x in an n-dimensional Euclidean space can be defined as an ordered list of n real numbers (the Cartesian coordinates of P): x = [x1, x2, ..., xn]. Its magnitude or length is most commonly defined as its Euclidean norm (or Euclidean length):

\|\mathbf{x}\| := \sqrt{x_1^2 + x_2^2 + \cdots + x_n^2}.

For instance, in a 3-dimensional space, the magnitude of [4, 5, 6] is √(42 + 52 + 62) = √77 or about 8.775. This is equivalent to the square root of the dot product of the vector by itself:

\|\mathbf{x}\| :=  \sqrt{\mathbf{x} \cdot \mathbf{x}}.

The Euclidean norm of a vector is just a special case of Euclidean distance: the distance between its tail and its tip. Two similar notations are used for the Euclidean norm of a vector x:

  1. \left \| \mathbf{x} \right \|,
  2. \left | \mathbf{x} \right |.

The second notation is generally discouraged, because it is also used to denote the absolute value of scalars and the determinants of matrices.

  Normed vector spaces

By definition, all Euclidean vectors have a magnitude (see above). However, the notion of magnitude cannot be applied to all kinds of vectors.

A function that maps objects to their magnitudes is called a norm. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. In high mathematics, not all vector spaces are normed.

  Logarithmic magnitudes

When comparing magnitudes, it is often helpful to use a logarithmic scale. Real-world examples include the loudness of a sound (decibel), the brightness of a star, or the Richter scale of earthquake intensity. Logarithmic magnitudes can be negative. It is usually not meaningful to simply add or subtract them.

  "Order of magnitude"

In advanced mathematics, as well as colloquially in popular culture, especially geek culture, the phrase "order of magnitude" is used to denote a change in a numeric quantity, usually a measurement, by a factor of 10; that is, the moving of the decimal point in a number one way or the other, possibly with the addition of significant zeros.

Occasionally the phrase "half an order of magnitude" is also used, generally in more informal contexts. Sometimes, this is used to denote a 5 to 1 change, or alternatively 101/2 to 1 (approximately 3.162 to 1).

  See also




All translations of Magnitude (mathematics)

sensagent's content

  • definitions
  • synonyms
  • antonyms
  • encyclopedia

Dictionary and translator for handheld

⇨ New : sensagent is now available on your handheld

   Advertising ▼

sensagent's office

Shortkey or widget. Free.

Windows Shortkey: sensagent. Free.

Vista Widget : sensagent. Free.

Webmaster Solution


A windows (pop-into) of information (full-content of Sensagent) triggered by double-clicking any word on your webpage. Give contextual explanation and translation from your sites !

Try here  or   get the code


With a SensagentBox, visitors to your site can access reliable information on over 5 million pages provided by Sensagent.com. Choose the design that fits your site.

Business solution

Improve your site content

Add new content to your site from Sensagent by XML.

Crawl products or adds

Get XML access to reach the best products.

Index images and define metadata

Get XML access to fix the meaning of your metadata.

Please, email us to describe your idea.


The English word games are:
○   Anagrams
○   Wildcard, crossword
○   Lettris
○   Boggle.


Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.


Boggle gives you 3 minutes to find as many words (3 letters or more) as you can in a grid of 16 letters. You can also try the grid of 16 letters. Letters must be adjacent and longer words score better. See if you can get into the grid Hall of Fame !

English dictionary
Main references

Most English definitions are provided by WordNet .
English thesaurus is mainly derived from The Integral Dictionary (TID).
English Encyclopedia is licensed by Wikipedia (GNU).


The wordgames anagrams, crossword, Lettris and Boggle are provided by Memodata.
The web service Alexandria is granted from Memodata for the Ebay search.
The SensagentBox are offered by sensAgent.


Change the target language to find translations.
Tips: browse the semantic fields (see From ideas to words) in two languages to learn more.

last searches on the dictionary :

4936 online visitors

computed in 0.156s

I would like to report:
section :
a spelling or a grammatical mistake
an offensive content(racist, pornographic, injurious, etc.)
a copyright violation
an error
a missing statement
please precise:



Company informations

My account



   Advertising ▼